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For two events A and B, P(A) = 0.5, P(B) = 0.35, and P(A/B) = 0.7. Select all of the correct statements.

AP(B/A) = 0.49
BP(B/A) = P(A/B)
CP(A ∩ B) = 0.245
DP(A ∩ B) = 0.35

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Answer: a. P(B/A) = 0.49

c. P(A ∩ B) = 0.245

Step-by-step explanation:

We know that for any dependent events A and B, the conditional probability of getting A given that B is given by :-

\(P(A|B)=\dfrac{P(A\cap B)}{P(B)}\)

Given: P(A) = 0.5, P(B) = 0.35, and P(A/B) = 0.7

\(\\\Rightarrow\ 0.7=\dfrac{P(\cap B)}{0.35}\\\\\Rightarrow\ P(A\cap B)=0.35\times0.7=0.245\)

Now, the conditional probability of getting B given that A is given by :-

\(P(B|A)=\dfrac{P(A\cap B)}{P(A)}\\\\\Rightarrow\ P(B|A)=\dfrac{0.245}{0.5}=0.49 eq P(A|B)\)

Hence, the correct statements are :

a. P(B/A) = 0.49

c. P(A ∩ B) = 0.245

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