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Question
Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find
- P (A and B)
- P(A and not B)
- P(A or B)
- P(neither A nor B)
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Solution
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
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