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. \[=P(A)+P(B)+P(C)-P(A\cap B)\] \[-P(B\cap C)-P(C\cap A)+P(A\cap B\cap C)\] \[=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}-0-0-\frac{1}{8}+0=\frac{5}{8}\]