A die is thrown three times. Find `P(A/B)` and `P(B/A),` if `A=4` appears on the third toss, `B=6` and `5` appear respectively on first two tosses.

Explanation

A shows 4 appears on third throw

B shows 6 appears on first throw and and 5 on second throw


`A={(1,1,4),(1,2,4),(1,3,4),(1,4,4),(1,5,4),(1,6,4),(2,1,4),(2,2,4),(2,3,4),(2,4,4),(2,5,4),(2,6,4),(6,1,4),(6,2,4),(6,3,4),(6,4,4),(6,5,4),(6,6,4)}`

`
B={6,5,1),(6,5,2),(6,5,3),(6,5,4),(6,5,5),(6,5,6)}`


Then,

`
A cap B={(6,5,4)}`
`
therefore P(A / B)=frac{n(A cap B)}{n(B)}=frac{1}{6}`

`
therefore P(B / A)=frac{n(A cap B)}{n(A)}=frac{1}{36}`