Question

If ​P(A)equals one half ​, ​P(B)equals three fifths ​, and P(B/A) equals one sixth ​, find P( A/B)

Answer 1

`(5)/(36)`

Explanation:

Given,

P(A) =
`(1)/(2)`,

P(B) =
`(3)/(5)`

`P((B)/(A))=(1)/(6)`

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

`\implies (P(A\cap B))/(P(A)) = (1)/(6)`

`(P(A\cap B))/((1)/(2))=(1)/(6)`

`2P(A\cap B) = (1)/(6)`

`\implies P(A\cap B) = (1)/(12)`

Now,

`P((A)/(B))=(P(A\cap B) )/(P(B))= (1/12)/(3/5)=(5)/(36)`