Question

Let A and B be independent events with P (A) = 0.3 and P (B) = 0.4. Find 

1. P (A ∩ B)
2. P (A ∪ B)
3. P (A | B)
4. P (B | A)

Answer 1

It is given that P (A) = 0.3 and P (B) = 0.4

If A and B are independent events, then

(i) P(A ∩ B) = P(A) · P(B)

P(A ∩ B) = 0.3 × 0.4

P(A ∩ B) = 0.12

(ii) P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∪ B) = 0.3 + 0.4 - 0.12

P(A ∪ B) = 0.58

(iii) P(A | B) = `(P(A ∩ B))/(P(B))`

P(A | B) = `0.12/0.4`

P(A | B) `= 3/10`

P(A | B) `= 0.3`

(iv) P(B | A) = `(P(A ∩ B))/(P(A))`

P(B | A) = `0.12/0.3`

P(B | A) = 0.4