Suppose you have a bag of 100 coins of which 1 is biased with both sides as Heads. You pick a coin from the bag and toss it three times. The result of all three tosses is Heads. What is the probability that the selected coin is biased?
My answer:-
P(selecting a biased coin) = 1/100
P(getting a head thrice with the biased coin) = 1
P(selecting an unbiased coin) = 99/100
P(getting a head thrice with the unbiased coin) = 1/8
P(selecting a biased coin|coin toss resulted in 3 heads) =
P(selecting a biased coin and getting heads thrice)/
[P(selecting a biased coin and getting heads thrice) +
P(selecting an unbiased coin and getting heads thrice)]
= (1/100)/[(1/100) + (99/800)]
= (1/100)/(107/800)
= 8/107
= 0.0747
Is this correct? Thanks.
homework
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