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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

Given P(A) = 0.3, P (B) = 0.6.
(i): Finding P (A and B):
If A and B are independent events, P(AB)=P(A)P(B)P(A∩B)=P(A)P(B)
P(AB)=P(A)P(B)P(A∩B)=P(A)P(B) = 0.3 ×× 0.6 = 0.18

(ii): Finding P (A and not B):
If A and B are independent events, A¯ and B¯ are also independent.
P(AB¯)=P(A)×P(B¯)=P(A)×(1P(B))=0.3×(10.6)=0.3×0.4=0.12⇒P(A∩B¯)=P(A)×P(B¯)=P(A)×(1−P(B))=0.3×(1−0.6)=0.3×0.4=0.12

(iii): Finding P (A or B):
P (A B) = P(A) + P(B) - P(A B)
P(AB)=0.3+0.60.18=0.72.⇒P(A∪B)=0.3+0.6−0.18=0.72.

(iv): Finding P (neither A nor B):
P (neither A nor B) = P (A¯B¯A¯∩B¯) = 1 - P (A B) = 1 - 0.72 = 0.28.

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