Is the coin you flipped more likely to be the fair coin or, Operation Management

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Is the coin you flipped more likely to be the fair coin or

Question

Suppose you are given two coins. The first coin is fair and the second coin comes up Heads 75% of the time. You choose one of the coins at random and flip it three times, yielding Heads, Heads, and Tails (HHT).

1. Is the coin you flipped more likely to be the fair coin or the unfair one?

2. Why?

Hint. To answer these questions, use Bayes' theorem for Pr(A|B) where

A is the event "the coin I flipped is fair"

B is the event "the outcome of three flips was HHT"

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