Question

If `P(A) = 6/11, P(B) = 5/11 "and"  P(A ∪ B) = 7/11` find

1. P(A ∩ B)
2. P(A|B)
3. P(B|A)

Answer 1

(i) Now, P(A) + P(B) - P(A ∩ B)= `7/11`

⇒ P(A ∩ B) = `6/11 + 5/11 - 7/11`

`= 4/11`

(ii) `P(A|B) = (P(A ∩ B))/(P(B))`

`= (4/11)/(5/11)`

`= 4/5`

(iii) `P (B|A) = (P(A ∩ B))/(P (A))`

`= (4/11)/(6/11)`

`= 4/6`

`= 2/3`