Question

According to the general equation for conditional probability, if P(AB) =

4/5
and P(B) = 5/6, what is P(AIB)?
A.15/16
B.35/36
C.8/9
D.24/25

Answer 1

`\sf D. \quad P(A|B)=(24)/(25)`

Explanation:

General equation for conditional probability

`\sf P(A \cap B)=P(A)\:P(B|A)`

As we need to find P(A|B) we can rewrite the equation:

`\implies \sf P(B \cap A)=P(B)\:P(A|B)`

Given:

`\sf P(A \cap B)=(4)/(5)`

`\sf P(B)=(5)/(6)`

Remember that
`\sf P(A \cap B)=P(B \cap A)`

Substitute the given values into the formula:

`\implies \sf P(B \cap A)=P(B)\:P(A|B)`

`\implies \sf (4)/(5)=(5)/(6)\:P(A|B)`

`\implies \sf P(A|B)=(4)/(5) / (5)/(6)`

`\implies \sf P(A|B)=(4)/(5) * (6)/(5)`

`\implies \sf P(A|B)=(24)/(25)`