SOLUTION: Hello! A coin is flipped three times. Let A be the event that the outcome of the first flip is a heads.Let B be the be the event that the outcomes of second and third flips are bot

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Question 763117: Hello! A coin is flipped three times. Let A be the event that the outcome of the first flip is a heads.Let B be the be the event that the outcomes of second and third flips are both tails.What is the probability that the outcomes of the second and third flips are both tails, given that the first one is a heads? Are A and B independent? Why or why not? Please!
Answer by reviewermath(1029) About Me  (Show Source):
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A coin is flipped three times. Let A be the event that the outcome of the first flip is a heads.Let B be the be the event that the outcomes of second and third flips are both tails.
What is the probability that the outcomes of the second and third flips are both tails, given that the first one is a heads?
P(B|A) = P(A ∩ B)/P(A)
= %280.5%5E3%29%2F0.5
= highlight%280.25%29
Are A and B independent? Why or why not?
A and B are independent because P(B|A) = P(B).
P(B|A) = 0.25 and P(B) = 0.25.