question_answer 1)
If the odds against an event be 2 : 3, then the probability of its occurrence is
A)
\[\frac{1}{5}\] done
clear
B)
\[\frac{2}{5}\] done
clear
C)
\[\frac{3}{5}\] done
clear
D)
1 done
clear
View Solution play_arrow
question_answer 2)
If the odds in favour of an event be 3 : 5, then the probability of non-occurrence of the event is
A)
\[\frac{3}{5}\] done
clear
B)
\[\frac{5}{3}\] done
clear
C)
\[\frac{3}{8}\] done
clear
D)
\[\frac{5}{8}\] done
clear
View Solution play_arrow
question_answer 3)
A card is drawn from a pack of 52 cards. A gambler bets that it is a spade or an ace. What are the odds against his winning this bet
A)
17 : 52 done
clear
B)
52 : 17 done
clear
C)
9 : 4 done
clear
D)
4 : 9 done
clear
View Solution play_arrow
question_answer 4)
An event has odds in favour 4 : 5, then the probability that event occurs, is
A)
\[\frac{1}{5}\] done
clear
B)
\[\frac{4}{5}\] done
clear
C)
\[\frac{4}{9}\] done
clear
D)
\[\frac{5}{9}\] done
clear
View Solution play_arrow
question_answer 5)
For an event, odds against is 6 : 5. The probability that event does not occur, is
A)
\[\frac{5}{6}\] done
clear
B)
\[\frac{6}{11}\] done
clear
C)
\[\frac{5}{11}\] done
clear
D)
\[\frac{1}{6}\] done
clear
View Solution play_arrow
question_answer 6)
In a horse race the odds in favour of three horses are \[1:2\], \[1:3\] and \[1:4\]. The probability that one of the horse will win the race is
A)
\[\frac{37}{60}\] done
clear
B)
\[\frac{47}{60}\] done
clear
C)
\[\frac{1}{4}\] done
clear
D)
\[\frac{3}{4}\] done
clear
View Solution play_arrow
question_answer 7)
The odds against a certain event is 5 : 2 and the odds in favour of another event is 6 : 5. If both the events are independent, then the probability that at least one of the events will happen is [RPET 1997]
A)
\[\frac{50}{77}\] done
clear
B)
\[\frac{52}{77}\] done
clear
C)
\[\frac{25}{88}\] done
clear
D)
\[\frac{63}{88}\] done
clear
View Solution play_arrow
question_answer 8)
If odds against solving a question by three students are 2 : 1, \[5:2\] and \[5:3\] respectively, then probability that the question is solved only by one student is [RPET 1999]
A)
\[\frac{31}{56}\] done
clear
B)
\[\frac{24}{56}\] done
clear
C)
\[\frac{25}{56}\] done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 9)
Three ships A, B and C sail from England to India. If the ratio of their arriving safely are 2 : 5, 3 : 7 and 6 : 11 respectively then the probability of all the ships for arriving safely is [Pb. CET 2000]
A)
\[\frac{18}{595}\] done
clear
B)
\[\frac{6}{17}\] done
clear
C)
\[\frac{3}{10}\] done
clear
D)
\[\frac{2}{7}\] done
clear
View Solution play_arrow
question_answer 10)
A party of 23 persons take their seats at a round table. The odds against two persons sitting together are [RPET 1999]
A)
10 : 1 done
clear
B)
1 : 11 done
clear
C)
9 : 10 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 11)
If two events A and B are such that \[P\,(A+B)=\frac{5}{6},\] \[P\,(AB)=\frac{1}{3}\,\] and \[P\,(\bar{A})=\frac{1}{2},\] then the events A and B are
A)
Independent done
clear
B)
Mutually exclusive done
clear
C)
Mutually exclusive and independent done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 12)
The probabilities of three mutually exclusive events are 2/3, 1/4 and 1/6. The statement is [MNR 1987; UPSEAT 2000]
A)
True done
clear
B)
Wrong done
clear
C)
Could be either done
clear
D)
Do not know done
clear
View Solution play_arrow
question_answer 13)
If A and B are two events such that \[P(A)=0.4\] , \[P\,(A+B)=0.7\] and \[P\,(AB)=0.2,\] then \[P\,(B)=\] [MP PET 1992]
A)
0.1 done
clear
B)
0.3 done
clear
C)
0.5 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 14)
Suppose that A, B, C are events such that \[P\,(A)=P\,(B)=P\,(C)=\frac{1}{4},\,P\,(AB)=P\,(CB)=0,\,P\,(AC)=\frac{1}{8},\] then \[P\,(A+B)=\] [MP PET 1992]
A)
0.125 done
clear
B)
0.25 done
clear
C)
0.375 done
clear
D)
0.5 done
clear
View Solution play_arrow
question_answer 15)
A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is [MP PET 1989]
A)
\[\frac{1}{13}\] done
clear
B)
\[\frac{1}{26}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{7}{13}\] done
clear
View Solution play_arrow
question_answer 16)
If the probability of X to fail in the examination is 0.3 and that for Y is 0.2, then the probability that either X or Y fail in the examination is [IIT 1989]
A)
0.5 done
clear
B)
0.44 done
clear
C)
0.6 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 17)
If \[P\,(A)=0.4,\,\,P\,(B)=x,\,\,P\,(A\cup B)=0.7\] and the events A and B are independent, then x = [CEE 1993]
A)
\[\frac{1}{3}\] done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{2}{3}\] done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 18)
If A and B are two events of a random experiment, \[P\,(A)=0.25\] , \[P\,(B)=0.5\] and \[P\,(A\cap B)=0.15,\] then \[P\,(A\cap \bar{B})=\] [MP PET 1987]
A)
0.1 done
clear
B)
0.35 done
clear
C)
0.15 done
clear
D)
0.6 done
clear
View Solution play_arrow
question_answer 19)
If \[P\,(A)=0.4,\,\,P\,(B)=x,\,\,P\,(A\cup B)=0.7\] and the events A and B are mutually exclusive, then \[x=\] [MP PET 1992]
A)
\[\frac{3}{10}\] done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{2}{5}\] done
clear
D)
\[\frac{1}{5}\] done
clear
View Solution play_arrow
question_answer 20)
If A and B are any two events, then the probability that exactly one of them occur is [BIT Ranchi 1990; IIT 1984; RPET 1995, 2002; MP PET 2004]
A)
\[P\,(A)+P\,(B)-P\,(A\cap B)\] done
clear
B)
\[P\,(A)+P\,(B)-2P\,(A\cap B)\] done
clear
C)
\[P\,(A)+P\,(B)-P\,(A\cup B)\] done
clear
D)
\[P\,(A)+P\,(B)-2P\,(A\cup B)\] done
clear
View Solution play_arrow
question_answer 21)
A coin is tossed twice. If events A and B are defined as : A = head on first toss, \[B=\] head on second toss. Then the probability of \[A\cup B=\]
A)
\[\frac{1}{4}\] done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{1}{8}\] done
clear
D)
\[\frac{3}{4}\] done
clear
View Solution play_arrow
question_answer 22)
If A and B are two mutually exclusive events, then \[P\,(A+B)=\] [MNR 1978; MP PET 1991, 92]
A)
\[P\,(A)+P\,(B)-P\,(AB)\] done
clear
B)
\[P\,(A)-P\,(B)\] done
clear
C)
\[P\,(A)+P\,(B)\] done
clear
D)
\[P\,(A)+P\,(B)+P\,(AB)\] done
clear
View Solution play_arrow
question_answer 23)
The probability of happening at least one of the events A and B is 0.6. If the events A and B happens simultaneously with the probability 0.2, then \[P\,(\bar{A})+P\,(\bar{B})=\] [Roorkee 1989; IIT 1987; MP PET 1997; DCE 2001; J & K 2005]
A)
0.4 done
clear
B)
0.8 done
clear
C)
1.2 done
clear
D)
1.4 done
clear
View Solution play_arrow
question_answer 24)
The chances to fail in Physics are 20% and the chances to fail in Mathematics are 10%. What are the chances to fail in at least one subject
A)
28% done
clear
B)
38% done
clear
C)
72% done
clear
D)
82% done
clear
View Solution play_arrow
question_answer 25)
If \[P\,(A)=\frac{1}{4},\,\,P\,(B)=\frac{5}{8}\] and \[P\,(A\cup B)=\frac{3}{4},\] then \[P\,(A\cap B)=\]
A)
\[\frac{1}{8}\] done
clear
B)
0 done
clear
C)
\[\frac{3}{4}\] done
clear
D)
1 done
clear
View Solution play_arrow
question_answer 26)
If A and B are two independent events such that \[P\,(A)=0.40,\,\,P\,(B)=0.50.\] Find \[P\](neither A nor B) [MP PET 1989; J & K 2005]
A)
0.90 done
clear
B)
0.10 done
clear
C)
0.2 done
clear
D)
0.3 done
clear
View Solution play_arrow
question_answer 27)
If A and B are two independent events, then \[P\,(A+B)=\] [MP PET 1992]
A)
\[P\,(A)+P\,(B)-P\,(A)\,P\,(B)\] done
clear
B)
\[P\,(A)-P\,(B)\] done
clear
C)
\[P\,(A)+P\,(B)\] done
clear
D)
\[P\,(A)+P\,(B)+P\,(A)\,P\,(B)\] done
clear
View Solution play_arrow
question_answer 28)
If an integer is chosen at random from first 100 positive integers, then the probability that the chosen number is a multiple of 4 or 6, is
A)
\[\frac{41}{100}\] done
clear
B)
\[\frac{33}{100}\] done
clear
C)
\[\frac{1}{10}\] done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 29)
If the probability of a horse A winning a race is 1/4 and the probability of a horse B winning the same race is 1/5, then the probability that either of them will win the race is
A)
\[\frac{1}{20}\] done
clear
B)
\[\frac{9}{20}\] done
clear
C)
\[\frac{11}{20}\] done
clear
D)
\[\frac{19}{20}\] done
clear
View Solution play_arrow
question_answer 30)
If A and B an two events such that \[P\,(A\cup B)=\frac{5}{6}\],\[P\,(A\cap B)=\frac{1}{3}\] and \[P\,(\bar{B})=\frac{1}{3},\] then \[P\,(A)=\]
A)
\[\frac{1}{4}\] done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{2}{3}\] done
clear
View Solution play_arrow
question_answer 31)
If A and B are two events such that \[P\,(A\cup B)\,+P\,(A\cap B)=\frac{7}{8}\] and \[P\,(A)=2\,P\,(B),\] then \[P\,(A)=\]
A)
\[\frac{7}{12}\] done
clear
B)
\[\frac{7}{24}\] done
clear
C)
\[\frac{5}{12}\] done
clear
D)
\[\frac{17}{24}\] done
clear
View Solution play_arrow
question_answer 32)
The probabilities that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is [CEE 1993; Pb. CET 2004]
A)
\[p+q\] done
clear
B)
\[p+q-2qp\] done
clear
C)
\[p+q-pq\] done
clear
D)
\[p+q+pq\] done
clear
View Solution play_arrow
question_answer 33)
A and B are two independent events. The probability that both A and B occur is \[\frac{1}{6}\] and the probability that neither of them occurs is \[\frac{1}{3}\]. Then the probability of the two events are respectively [Roorkee 1989]
A)
\[\frac{1}{2}\]and \[\frac{1}{3}\] done
clear
B)
\[\frac{1}{5}\]and \[\frac{1}{6}\] done
clear
C)
\[\frac{1}{2}\]and \[\frac{1}{6}\] done
clear
D)
\[\frac{2}{3}\]and \[\frac{1}{4}\] done
clear
View Solution play_arrow
question_answer 34)
If A and B are two independent events such that \[P\,(A\cap B')=\frac{3}{25}\] and \[P\,(A'\cap B)=\frac{8}{25},\] then \[P(A)=\] [IIT Screening]
A)
\[\frac{1}{5}\] done
clear
B)
\[\frac{3}{8}\] done
clear
C)
\[\frac{2}{5}\] done
clear
D)
\[\frac{4}{5}\] done
clear
View Solution play_arrow
question_answer 35)
Let A and B be two events such that \[P\,(A)=0.3\] and \[P\,(A\cup B)=0.8\]. If A and B are independent events, then \[P(B)=\] [IIT 1990; UPSEAT 2001, 02]
A)
\[\frac{5}{6}\] done
clear
B)
\[\frac{5}{7}\] done
clear
C)
\[\frac{3}{5}\] done
clear
D)
\[\frac{2}{5}\] done
clear
View Solution play_arrow
question_answer 36)
For two given events A and B, \[P\,(A\cap B)=\] [IIT 1988]
A)
Not less than \[P(A)+P\,(B)-1\] done
clear
B)
Not greater than \[P(A)+P(B)\] done
clear
C)
Equal to \[P(A)+P(B)-P(A\cup B)\] done
clear
D)
All of the above done
clear
View Solution play_arrow
question_answer 37)
\[P(A\cup B)=P(A\cap B)\]if and only if the relation between \[P(A)\] and \[P(B)\] is [IIT 1985]
A)
\[P(A)=P(\bar{A})\] done
clear
B)
\[P\,(A\cap B)=P(A'\cap B')\] done
clear
C)
\[P\,(A)=P\,(B)\] done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 38)
The two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is [IIT 1980; MP PET 1994]
A)
0.39 done
clear
B)
0.25 done
clear
C)
0.904 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 39)
Twelve tickets are numbered 1 to 12. One ticket is drawn at random, then the probability of the number to be divisible by 2 or 3, is
A)
\[\frac{2}{3}\] done
clear
B)
\[\frac{7}{12}\] done
clear
C)
\[\frac{5}{6}\] done
clear
D)
\[\frac{3}{4}\] done
clear
View Solution play_arrow
question_answer 40)
Three athlete A, B and C participate in a race competetion. The probability of winning A and B is twice of winning C. Then the probability that the race win by A or B, is
A)
\[\frac{2}{3}\] done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{4}{5}\] done
clear
D)
\[\frac{1}{3}\] done
clear
View Solution play_arrow
question_answer 41)
If \[P(A)=\frac{1}{2},\,\,P(B)=\frac{1}{3}\] and \[P(A\cap B)=\frac{7}{12},\] then the value of \[P\,({A}'\cap {B}')\] is
A)
\[\frac{7}{12}\] done
clear
B)
\[\frac{3}{4}\] done
clear
C)
\[\frac{1}{4}\] done
clear
D)
\[\frac{1}{6}\] done
clear
View Solution play_arrow
question_answer 42)
In a city 20% persons read English newspaper, 40% read Hindi newspaper and 5% read both newspapers. The percentage of non-reader either paper is
A)
60% done
clear
B)
35% done
clear
C)
25% done
clear
D)
45% done
clear
View Solution play_arrow
question_answer 43)
The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then \[P({A}')+P({B}')=\]
A)
0.9 done
clear
B)
1.15 done
clear
C)
1.1 done
clear
D)
1.2 done
clear
View Solution play_arrow
question_answer 44)
The probability that a man will be alive in 20 years is \[\frac{3}{5}\] and the probability that his wife will be alive in 20 years is \[\frac{2}{3}\]. Then the probability that at least one will be alive in 20 years, is [Bihar CEE 1994]
A)
\[\frac{13}{15}\] done
clear
B)
\[\frac{7}{15}\] done
clear
C)
\[\frac{4}{15}\] done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 45)
Given two mutually exclusive events A and B such that \[P(A)=0.45\] and \[P(B)=0.35,\] then P (A or B) = [AI CBSE 1979]
A)
0.1 done
clear
B)
0.25 done
clear
C)
0.15 done
clear
D)
0.8 done
clear
View Solution play_arrow
question_answer 46)
If A and B are any two events, then \[P(A\cup B)=\] [MP PET 1995]
A)
\[P(A)+P(B)\] done
clear
B)
\[P(A)+P(B)+P(A\cap B)\] done
clear
C)
\[P(A)+P(B)-P(A\cap B)\] done
clear
D)
\[P(A)\,\,.\,\,P(B)\] done
clear
View Solution play_arrow
question_answer 47)
If \[{{A}_{1}},\,{{A}_{2}},...{{A}_{n}}\] are any n events, then
A)
\[P\,({{A}_{1}}\cup {{A}_{2}}\cup ...\cup {{A}_{n}})=P\,({{A}_{1}})+P({{A}_{2}})+...+P\,({{A}_{n}})\] done
clear
B)
\[P\,({{A}_{1}}\cup {{A}_{2}}\cup ...\cup {{A}_{n}})>P\,({{A}_{1}})+P({{A}_{2}})+...+P\,({{A}_{n}})\] done
clear
C)
\[P\,({{A}_{1}}\cup {{A}_{2}}\cup ...\cup {{A}_{n}})\le P\,({{A}_{1}})+P({{A}_{2}})+...+P\,({{A}_{n}})\] done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 48)
In a class of 125 students 70 passed in Mathematics, 55 in Statistics and 30 in both. The probability that a student selected at random from the class has passed in only one subject is [EAMCET 1993]
A)
\[\frac{13}{25}\] done
clear
B)
\[\frac{3}{25}\] done
clear
C)
\[\frac{17}{25}\] done
clear
D)
\[\frac{8}{25}\] done
clear
View Solution play_arrow
question_answer 49)
A, B, C are any three events. If P (S) denotes the probability of S happening then \[P\,(A\cap (B\cup C))=\] [EAMCET 1994]
A)
\[P(A)+P(B)+P(C)-P(A\cap B)-P(A\cap C)\] done
clear
B)
\[P(A)+P(B)+P(C)-P(B)\,P(C)\] done
clear
C)
\[P(A\cap B)+P(A\cap C)-P(A\cap B\cap C)\] done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 50)
Let \[{{E}_{1}},{{E}_{2}},{{E}_{3}}\]be three arbitrary events of a sample space S. Consider the following statements which of the following statements are correct [Pb. CET 2004]
A)
P (only one of them occurs) \[=P({{\bar{E}}_{1}}{{E}_{2}}{{E}_{3}}+{{E}_{1}}{{\bar{E}}_{2}}{{E}_{3}}+{{E}_{1}}{{E}_{2}}{{\overline{E}}_{3}})\] done
clear
B)
P (none of them occurs) \[=P({{\overline{E}}_{1}}+{{\overline{E}}_{2}}+{{\overline{E}}_{3}})\] done
clear
C)
P (at least one of them occurs) \[=P({{E}_{1}}+{{E}_{2}}+{{E}_{3}})\] done
clear
D)
P (all the three occurs)\[=P({{E}_{1}}+{{E}_{2}}+{{E}_{3}})\] where \[P({{E}_{1}})\]denotes the probability of \[{{E}_{1}}\] and \[{{\bar{E}}_{1}}\] denotes complement of \[{{E}_{1}}\]. done
clear
View Solution play_arrow
question_answer 51)
One card is drawn from a pack of 52 cards. The probability that it is a queen or heart is [RPET 1999]
A)
\[\frac{1}{26}\] done
clear
B)
\[\frac{3}{26}\] done
clear
C)
\[\frac{4}{13}\] done
clear
D)
\[\frac{3}{13}\] done
clear
View Solution play_arrow
question_answer 52)
The probabilities of occurrence of two events are respectively 0.21 and 0.49. The probability that both occurs simultaneously is 0.16. Then the probability that none of the two occurs is [MP PET 1998]
A)
0.30 done
clear
B)
0.46 done
clear
C)
0.14 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 53)
Let A and B be events for which \[P(A)=x\], \[P(B)=y,\]\[P(A\cap B)=z,\] then \[P(\bar{A}\cap B)\] equals [AMU 1999]
A)
\[(1-x)\,y\] done
clear
B)
\[1-x+\,y\] done
clear
C)
y ? z done
clear
D)
\[1-x+y-z\] done
clear
View Solution play_arrow
question_answer 54)
The probability of solving a question by three students are \[\frac{1}{2},\,\,\frac{1}{4},\,\,\frac{1}{6}\] respectively. Probability of question is being solved will be [UPSEAT 1999]
A)
\[\frac{33}{48}\] done
clear
B)
\[\frac{35}{48}\] done
clear
C)
\[\frac{31}{48}\] done
clear
D)
\[\frac{37}{48}\] done
clear
View Solution play_arrow
question_answer 55)
Let A and B are two independent events. The probability that both A and B occur together is 1/6 and the probability that neither of them occurs is 1/3. The probability of occurrence of A is [RPET 2000]
A)
0 or 1 done
clear
B)
\[\frac{1}{2}\] or \[\frac{1}{3}\] done
clear
C)
\[\frac{1}{2}\] or \[\frac{1}{4}\] done
clear
D)
\[\frac{1}{3}\] or \[\frac{1}{4}\] done
clear
View Solution play_arrow
question_answer 56)
One card is drawn randomly from a pack of 52 cards, then the probability that it is a king or spade is [RPET 2001]
A)
\[\frac{1}{26}\] done
clear
B)
\[\frac{3}{26}\] done
clear
C)
\[\frac{4}{13}\] done
clear
D)
\[\frac{3}{13}\] done
clear
View Solution play_arrow
question_answer 57)
If \[P(A)=0.25,\,\,P(B)=0.50\] and \[P(A\cap B)=0.14,\] then \[P(A\cap \bar{B})\] is equal to [RPET 2001]
A)
0.61 done
clear
B)
0.39 done
clear
C)
0.48 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 58)
If A and B are any two events, then \[P(\bar{A}\cap B)=\] [MP PET 2001]
A)
\[P(\bar{A})\,\,\,P(\bar{B})\] done
clear
B)
\[1-P(A)-P(B)\] done
clear
C)
\[P(A)+P(B)-P(A\cap B)\] done
clear
D)
\[P(B)-P(A\cap B)\] done
clear
View Solution play_arrow
question_answer 59)
In two events \[P(A\cup B)=5/6\], \[P({{A}^{c}})=5/6\], \[P(B)=2/3,\] then A and B are [UPSEAT 2001]
A)
Independent done
clear
B)
Mutually exclusive done
clear
C)
Mutually exhaustive done
clear
D)
Dependent done
clear
View Solution play_arrow
question_answer 60)
The probability that at least one of the events A and B occurs is 3/5. If A and B occur simultaneously with probability 1/5, then \[P({A}')+P({B}')\] is [DCE 2002]
A)
\[\frac{2}{5}\] done
clear
B)
\[\frac{4}{5}\] done
clear
C)
\[\frac{6}{5}\] done
clear
D)
\[\frac{7}{5}\] done
clear
View Solution play_arrow
question_answer 61)
If A and B are arbitrary events, then [DCE 2002]
A)
\[P(A\cap B)\ge P(A)+P(B)\] done
clear
B)
\[P(A\cup B)\le P(A)+P(B)\] done
clear
C)
\[P(A\cap B)=P(A)+P(B)\] done
clear
D)
None of these done
clear
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question_answer 62)
If A and B are events such that \[P(A\cup B)=3/4,\] \[P(A\cap B)=1/4,\] \[P(\bar{A})=2/3,\] then \[P(\bar{A}\cap B)\] is [AIEEE 2002]
A)
\[\frac{5}{12}\] done
clear
B)
\[\frac{3}{8}\] done
clear
C)
\[\frac{5}{8}\] done
clear
D)
\[\frac{1}{4}\] done
clear
View Solution play_arrow
question_answer 63)
A random variable X has the probability distribution
X 1 2 3 4 5 6 7 8 P(X) 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05
For the events \[E=\{X\]is prime number} and \[F=\{X<4\}\], the probability of \[P(E\cup F)\] is [AIEEE 2004]
A)
0.50 done
clear
B)
0.77 done
clear
C)
0.35 done
clear
D)
0.87 done
clear
View Solution play_arrow
question_answer 64)
If \[P(A)=P(B)=x\] and \[P(A\cap B)=P({A}'\cap {B}')=\frac{1}{3}\], then \[x=\] [UPSEAT 2003]
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{1}{4}\] done
clear
D)
\[\frac{1}{6}\] done
clear
View Solution play_arrow
question_answer 65)
If \[P(A\cup B)=0.8\] and \[P(A\cap B)=0.3,\] then \[P(\bar{A})+P(\bar{B})=\] [EAMCET 2003]
A)
0.3 done
clear
B)
0.5 done
clear
C)
0.7 done
clear
D)
0.9 done
clear
View Solution play_arrow
question_answer 66)
In a certain population 10% of the people are rich, 5% are famous and 3% are rich and famous. The probability that a person picked at random from the population is either famous or rich but not both, is equal to [UPSEAT 2004]
A)
0. 07 done
clear
B)
0.08 done
clear
C)
0. 09 done
clear
D)
0. 12 done
clear
View Solution play_arrow
question_answer 67)
A card is drawn from a pack of cards. Find the probability that the card will be a queen or a heart [RPET 2003]
A)
\[\frac{4}{3}\] done
clear
B)
\[\frac{16}{3}\] done
clear
C)
\[\frac{4}{13}\] done
clear
D)
\[\frac{5}{3}\] done
clear
View Solution play_arrow
question_answer 68)
Let A and B be two events such that \[P\overline{(A\cup B)}=\frac{1}{6},P(A\cap B)=\frac{1}{4}\] and \[P(\bar{A})=\frac{1}{4},\] where \[\bar{A}\] stands for complement of event A. Then events A and B are [AIEEE 2005]
A)
Independent but not equally likely done
clear
B)
Mutually exclusive and independent done
clear
C)
Equally likely and mutually exclusive done
clear
D)
Equally likely but not independent done
clear
View Solution play_arrow
question_answer 69)
Let S be a set containing n elements and we select 2 subsets A and B of S at random then the probability that \[A\cup B=S\] and \[A\cap B=\varphi \] is [Orissa JEE 2005]
A)
\[{{2}^{n}}\] done
clear
B)
\[{{n}^{2}}\] done
clear
C)
1/n done
clear
D)
\[1/{{2}^{n}}\] done
clear
View Solution play_arrow
question_answer 70)
Let A and B are two events and \[P({A}')=0.3\], \[P(B)=0.4,\,P(A\cap {B}')=0.5\], then \[P(A\cup {B}')\] is [Orissa JEE 2005]
A)
0.5 done
clear
B)
0.8 done
clear
C)
1 done
clear
D)
0.1 done
clear
View Solution play_arrow