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+1 vote
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in Introduction to Probability Theory by (47.8k points)
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If two events A and B are independent such that P(A) = 0.35 and P(A ∪ B) = 0.6, then P(B) is …

(a) 5/13

(b) 1/13

(c) 4/13

(d) 7/13

1 Answer

+1 vote
by (47.4k points)
selected by
 
Best answer

(a) 5/13

Given A and B are independent 

P(A ∩ B) = P(A) + P(B) 

⇒ Now P(A ∪ B) = P(A) + P(B) – P(A ∩ B) 

(i.e.,) Now P(A ∪ B) = P(A) + P(B) – P(A).P(B) 

0.6 = 0.35 + P(B) – (0.35) P(B) 

⇒ P(B) = (1 – 0.35) = 0.6 – 0.35 

0.65 P(B) = 0.25 

∴ P(B) = 0.25/0.65 = 25/65 = 5/13

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