Three fair coins are tossed simultaneously until all three show that same face. What is the probability that they are tossed more than three times?
Three fair coins are tossed simultaneously until all three show that same face. What is the probability that they are tossed more than three times?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 1YT
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Three fair coins are tossed simultaneously until all three show that same face. What is the
Is my answer correct?
Under geometric distribution: P(X>=t) = (1-p)t; t=number of failures before first success
All the possible outcomes in one toss: HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
p=P(all three coins are the same face in one toss) = 2/8 = 1/4
Toss 1: Fail, Toss 2: Fail, Toss 3: Fail, Toss 4: Success
P(X>=3) = (1-1/4)3 = 0.421875
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