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

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)=(P(A\cap B))/(P(B))`

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

`\\\Rightarrow\ 0.7=(P(\cap B))/(0.35)\\\\\Rightarrow\ P(A\cap B)=0.35*0.7=0.245`

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

`P(B|A)=(P(A\cap B))/(P(A))\\\\\Rightarrow\ P(B|A)=(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