JEE Main & Advanced
Sample Paper
JEE Main Sample Paper-39
question_answer
The probability of A = Probability of B = Probability of\[P(A)\cap P(B)\cap P(C)=0,\,\,P(B\cap C)=0\]and\[P(A\cap C)=\frac{1}{8},P(A\cap B)=0\]the probability that at least one of the events A, B, C exists is
A) \[\frac{5}{8}\]
B) \[\frac{37}{64}\]
C) \[\frac{3}{4}\]
D) 1
Correct Answer:
A
Solution :
\[\therefore \]Probability that at least one of the events A, B, C exists is given by the shaded region. Req. prob. \[=P(A)+P(B)+P(C)-P(A\cap B)\] \[-P(B\cap C)-P(C\cap A)+P(A\cap B\cap C)\] \[=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}-0-0-\frac{1}{8}+0=\frac{5}{8}\]