value: 10.00 points Christine Wong has asked Dave and Mike to help her move into

Question

value: 10.00 points Christine Wong has asked Dave and Mike to help her move into a new apartment on Sunday moming. She has asked them both in case one of them does not show up. From past experience, Christine knows that there is a 55% chance that Dave will not show up and a 45% chance that Mike will not show up. Dave and Mike do not know each other and their decisions can be assumed to be indepdndent. a. What is the probability that both Dave and Mike will show up? (Round your answer to 2 decimal places.) Probability b. What is the probability that at least one of them will show up? (Round your answer to 2 decimal places.) Probability c. What is the probability that neither Dave nor Mike will show up? (Round your answer to 2 decimal places.) Probability Hints eBook &Resources; Hint #1

Explanation / Answer

a)

Since the decisions are independent, so

P(Both Dave and Mike will show up) = P(Dave shows up) . P(Mike shows up) = (1-0.55)(1-0.45) = 0.2475 = 0.25 (approximately)

b)

P(at least one of them shows up) = 1 - P(No one of them shows up) = 1 - P(Dave does not show up) . P(Mike does not show up) = 1 - (0.55)(0.45) = 0.7525 = 0.75 (approximately)

c)

P(Neither Dave nor Mike shows up) = P(Dave does not shows up ) . P(Mike does not show up) = (0.55)(0.45) = 0.2475 = 0.25 (approximately)

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