10th Class Mathematics Probability Question Bank

done Assertion And Reason (MCQs) - Probability Total Questions - 20

• question_answer1)

  Directions (Q. Nos 1 - 20): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:

  Assertion (A): If a box contains 5 white, 2 red and 4 black marbles, then the probability of not drawing a white marble from the box is \[\frac{5}{11}\]

  Reason (R): \[P(\bar{E})=1-P(E),\] where E is any event.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer2)

  Assertion (A): When two coins are tossed simultaneously then the probability of getting no tail is \[\frac{1}{4}\].

  Reason (R): The probability of getting a head (i.e., no tail) in one toss of a coin is \[\frac{1}{2}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer3)

  Assertion (A): In a single throw of a die. The probability of getting a number Less than 7 is 1.

  Reason (R): The probability of a certain event is 1.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer4)

  Assertion (A): Two players Sania and Deepika play a tennis match. If the probability of Sania winning the match is \[0.\text{68},\] then the probability of Deepika winning the match is\[0.\text{32}\].

  Reason (R): The sum of the probability of two complementary events is 1.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer5)

  Assertion (A): An event is very unlikely to happen. Its probability is \[0.000\text{1}\]

  Reason (R): If P (A) denote the probability of a event A then \[0\le P(A)\le 1\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer6)

  Assertion (A): If the probability of an event is P then probability of its complementary event will be\[1-P\].

  Reason (R): When E and \[\bar{E}\] are complementary events, then \[P(\bar{E})+P(\bar{E})=1\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer7)

  Assertion (A): Cards numbered 5 to 102 are placed in a box. If a card is selected at random from the box, then the probability that the card selected has a number which is a perfect square, is \[\frac{4}{49}\].

  Reason (R): Probability of an event E is a number \[P(E)\]such that \[0\le P(E)\le 1\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer8)

  Assertion (A): Two dice are thrown simultaneously. There are 11 possible outcomes of their sum (3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13) and each of them are equally Likely.

  Reason (R): Probability of an event f is defined as \[P(E)=\frac{\text{Number of outcomes favourable to E}}{\text{Total number of possible outcomes}}\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer9)

  Assertion (A): If a die is thrown, the probability of getting a number less than 3 and greater than 2 is zero.

  Reason (R): Probability of an impossible event is zero.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer10)

  Assertion (A): In a simultaneously throw of a pair of dice. The probability of getting a double is \[\frac{1}{6}\].

  Reason (R): Probability of an event may be negative.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer11)

  Assertion (A): Three unbiased coins are tossed together, then the probability of getting exactly 1 head is \[\frac{3}{8}\].

  Reason (R): Favourable number of outcomes do not lie in the sample space of total number of outcomes.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer12)

  Assertion (A): Seven face cards are removed from a deck of cards and the cards are well shuffled. Then the probability of drawing a face card is \[\frac{5}{52}\].

  Reason (R): King, Queen and Jack are known as face cards.

  So, there are 12 face cards in total.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer13)

  Assertion (A): The probability of winning a game is \[0.\text{4},\]then the probability of losing it, is\[0.\text{6}\].

  Reason (R): \[P(E)+P(not\,E)=1.\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer14)

  Assertion (A): In rolling a dice, the probability of getting number 8 is zero.

  Reason (R): It’s an impossible event.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer15)

  Assertion (A): Two dice are rolled simultaneously. Then the probability of getting prime number on both dice is \[\frac{1}{4}\].

  Reason (R): Sum of probability of all the elementary events of a experiment is zero.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer16)

  Assertion (A): In a game, the entry fee is Rs.10. The game consists of tossing of 5 coins. If one or two heads show, Amita with the game and gets entry fee. The probability, the she gets the entry fee is \[\frac{3}{4}\].

  Reason (R): When three coins are tossed together, all the outcomes are {HHH, HHT, HTH, THH, HTT, THT, TTH and TTT}.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer17)

  Assertion (A): Card numbered as \[\text{1},\text{ 2},\text{ 3},.........1\text{5}\] are put in a box and mixed thoroughly, once card is then drawn at random. The probability of drawing an even number is \[\frac{1}{2}\].

  Reason (R): For any event E, we have \[0\le P(E)\le 1\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).   done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer18)

  Assertion (A): A number is selected from the numbers 1 to 20. The probability that it will be a prime is \[\frac{2}{5}\].

  Reason (R): There exists 25 prime numbers from natural number 1 to 100.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer19)

  Assertion (A): The probability of getting a prime number.

  When a die is thrown once is \[\frac{2}{3}\].

  Reason (R): Prime numbers on a dice are 2, 3, 5.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer20)

  Assertion (A): Consider a pack of cards that are numbered from 1 to 52. If a card is drawn at random from the pack, then the probability that it will have a prime number is \[\frac{7}{26}\].

  Reason (R): From 1 to 52, there are 15 prime numbers.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).   done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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