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in Introduction to Probability Theory by (47.8k points)
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The probability of two events A and B are 0.3 and 0.6 respectively. The probability that both A and B occur simultaneously is 0.18. The probability that neither A nor B occurs is …

(a) 0.1

(b) 0.72 

(c) 0.42 

(d) 0.28

1 Answer

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Best answer

(d) 0.28

P(A) = 0.3, P(B) = 0.6 

P(A ∩ B) = 0.18 

So P(A ∪ B) = P(A) + P(B) – P(A ∩ B) 

= 0.3 + 0.6 – 0.18 

= 0.9 – 0.18 = 0.72

P(A’ ∩ B’) = P[(A ∪ B)’] = 1 – P(A ∪ B) 

= 1 – 0.72 = 0.28

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