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# What is the probability of obtaining exactly four tails in five flips of a coin if at least three are tails?

We need to determine the separate event.

Let A = obtaining four tails in five flips of coin

Let B = obtaining at least three tails in five flips of coin

Apply Binomial Theorem for this problem, and we have:

P(A | B) = P(A ∩ B) / P(B)

P(A | B) means the probability of "given event B, or if event B occurs, then event A occurs."

P(A ∩ B) means the probability in which both event B and event A occur at a same time.

P(B) means the probability of event B occurs.

Work out each term...

P(B) = (5 choose 3)(½)³(½)² + (5 choose 4)(½)4(½) + (5 choose 5)(½)5(½)0

It's obvious that P(A ∩ B) = (5 choose 4)(½)4(½) since A ∩ B represents events A and B occurring at the same time, so there must be four tails occurring in five flips of coin.

Hence, you should get:

P(A | B) = P(A ∩ B) / P(B)

= ((5 choose 4)(½)4(½))/((5 choose 3)(½)³(½)² + (5 choose 4)(½)4(½) + (5 choose 5)(½)5(½)0) Study guides

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