Probability Question 355
Question: 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]
Options:
A) $ P(A)+P(B)+P(C)-P(A\cap B)-P(A\cap C) $
B) $ P(A)+P(B)+P(C)-P(B)P(C) $
C) $ P(A\cap B)+P(A\cap C)-P(A\cap B\cap C) $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ P[A\cap (B\cup C)]=P[(A\cap B)\cup (A\cap C)] $
$ =P(A\cap B)+P(A\cap C)-P[(A\cap B)\cap (A\cap C)] $
$ =P(A\cap B)+P(A\cap C)-P(A\cap B\cap C) $ .
BETA
