[3] There are two coins in a box; one coin is a fair coin, and the other is a bi

Question

[3] There are two coins in a box; one coin is a fair coin, and the other is a biased coin that comes up heads 75 percent of the time. Fiona chooses a coin at random and tosses it.

b) What is the probability that the chosen coin flips heads? (use the Law of Total Probability)

c) Given that the chosen coin flips heads, what is the conditional probability that it was the biased coin? (use Bayes' Theorem)

d) Given that the chosen coin flips tails, what is the conditional probability that it was the biased coin?

Explanation / Answer

b)probability that the chosen coin flips heads =p(fair coin and head+baised coin and head)=(1/2)*0.5+(1/2)*0.75=0.625

c) Given that the chosen coin flips heads, conditional probability that it was the biased coin=(1/2)*0.75/0.625=0.6

d)probability that the chosen coin flips tails =p(fair coin and tail+baised coin and tail)=(1/2)*0.5+(1/2)*0.25=0.375

Given that the chosen coin flips tails,conditional probability that it was the biased coin=(1/2)*0.25/0.375=0.3333

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