Question

Select all that apply.

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.

a. P(B/A) = 0.49
b. P(B/A) = P(A/B)
c. P(A ∩ B) = 0.245
d. P(A ∩ B) = 0.35

Answer 1

answer is below :-).......

Answer 2

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 :-

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

Hence, the correct statements are :

a. P(B/A) = 0.49

c. P(A ∩ B) = 0.245