Question

According to the general equation for conditional probability, if (image attached)

A.
`(40)/(49)`
B.
`(24)/(49)`
C.
`(32)/(49)`
D.
`(16)/(49)`

Answer 1

Correct choice is A.
`P(A|B)=(40)/(49)`.

Explanation:

Given that
`P(A\cap B)=(5)/(7)`,
`P(B)=(7)/(8)`.

Now using those values , we need to find the value of
`P(A|B)`.

So apply the formula of conditional probability:

`P(A\cap B)=P(B) * P(A|B)`

Plug the given values into above formula, we get:

`(5)/(7)=(7)/(8) * P(A|B)`

`(7)/(8) * P(A|B)=(5)/(7)`

`P(A|B)=((5)/(7))/((7)/(8))`

`P(A|B)=(5)/(7)\cdot(8)/(7)`

`P(A|B)=(40)/(49)`

Hence correct choice is A.
`P(A|B)=(40)/(49)`.

Answer 2

Answer: Option A

`P(A|B) = (40)/(49)`

Explanation:

In a probabilistic experiment, when two events A and B are dependent on each other, then the probability of occurrence A since B occurs is:

`P(A|B) = (P(A\ and\ B))/(P(B))`

Then if
`P(A\ and\ B) = (5)/(7)` and
`P(B) = (7)/(8)` then:

`P(A|B) = ((5)/(7))/((7)/(8))\\\\P(A|B) = (40)/(49)`