One of two biased coins A and B is selected and flipped 3 times. Let A be the event that coin A is selected and B be the event that coin B is selected, with probabilities p(A) = 0.4 and p(B) = 0.6. When coin A is flipped, the probability of heads is 0.2. When coin B is flipped, the probability of heads is 0.8. Let HHH be the event that the selected coin comes up heads 3 times. Complete the values X, Y, and Z in Bayes' Theorem to determine the probability coin B was chosen if all 3 flips come up heads. X Ex: 0.123-0.6 p(B|HHH) = Ex: 0.123 Y 0.6+Ex: 0.123 Ꮓ . 0.4

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter12: Review Of Calculus And Probability
Section12.5: Random Variables, Mean, Variance, And Covariance
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One of two biased coins A and B is selected and flipped 3 times. Let A be the event that coin A is
selected and B be the event that coin B is selected, with probabilities p(A) = 0.4 and p(B) = 0.6.
When coin A is flipped, the probability of heads is 0.2.
When coin B is flipped, the probability of heads is 0.8.
Let HHH be the event that the selected coin comes up heads 3 times. Complete the values X, Y, and Z
in Bayes' Theorem to determine the probability coin B was chosen if all 3 flips come up heads.
X
Ex: 0.123-0.6
p(B|HHH) =
Ex: 0.123
Y
0.6+Ex: 0.123
Ꮓ
.
0.4
Transcribed Image Text:One of two biased coins A and B is selected and flipped 3 times. Let A be the event that coin A is selected and B be the event that coin B is selected, with probabilities p(A) = 0.4 and p(B) = 0.6. When coin A is flipped, the probability of heads is 0.2. When coin B is flipped, the probability of heads is 0.8. Let HHH be the event that the selected coin comes up heads 3 times. Complete the values X, Y, and Z in Bayes' Theorem to determine the probability coin B was chosen if all 3 flips come up heads. X Ex: 0.123-0.6 p(B|HHH) = Ex: 0.123 Y 0.6+Ex: 0.123 Ꮓ . 0.4
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