SOLUTION: A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 4 times, what is the probability of getting a. exactly 2 tails? b. at least 3 heads

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Question 778464: A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 4 times, what is the probability of getting
a. exactly 2 tails?
b. at least 3 heads?

Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 4 times, what is the probability of getting
P(H) = 2P(T)
P(H) + P(T) = 1
2P(T) + P(T) = 1
3P(T) = 1
P(T) = 1%2F3 and P(H) = 2%2F3
a. exactly 2 tails?
X~Binomial(4, 1/3)
P(X = 2) = %28matrix%282%2C1%2C4%2C2%29%29%281%2F3%29%5E2%2A%282%2F3%29%5E2 = highlight%280.2963%29
b. at least 3 heads?
Y~Binomial(4, 2/3)
P(Y≥3) = = highlight%280.5926%29