Question

Events A, B, and C are independent. P(A) = 0.15 P(B) = 0.3 P(C) = 0.4...

Events A, B, and C are independent. P(A) = 0.15 P(B) = 0.3 P(C) = 0.4

a) probability that all events occur

b) Probability that at least one occurs

c) Probability that none occurs

d) Probability that exactly one event occurs

Math   Statistics-And-Probability   
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Answer #1

Given:-

Events A, B, and C are independent.

P(A) = 0.15 P(B) = 0.3 P(C) = 0.4

a) probability that all events occur?

Probability that all events occur = P(A and B and C) = P(A) * P(B) * P(C)

= 0.15 * 0.3 * 0.4

= 0.018

b) Probability that at least one occurs?

Probability that at least one occurs = P(A) + P(B) + P(C) - P(A and B and C)

= 0.15 + 0.3 + 0.4 - 0.018

= 0.832

c) Probability that none occurs?

Probability that none occurs = 1 - P(A and B and C)

= 1 - 0.018

= 0.982

d) Probability that exactly one event occurs?

Probability that exactly one event occurs:-

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