Question

Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find 

1. P (A and B)
2. P(A and not B)
3. P(A or B)
4. P(neither A nor B)

Answer 1

It is given that P (A) = 0.3 and P (B) = 0.6

Also, A and B are independent events.

(i) ∴ P(A and B) = P(A) · P(B)

⇒ P(A ∩ B) = 0.3 × 0.6

P(A ∩ B) = 0.18

(ii) P(A and not B) = P(A ∩ B')

= P(A) - P(A ∩ B)

= 0.3 - 0.18

= 0.12

(iii) P(A or B) = P(A ∪ B)

= P(A) + P(B) - P(A ∩ B)

= 0.3 + 0.6 - 0.18

= 0.72

(iv) P(niether A nor B) = P(A' ∩ B')

= P((A' ∩ B'))

= 1 - P(A ∪ B)

= 1 - 0.72

= 0.28