The probability that you picked the fair coin given that the outcome of the toss was heads is 1/3.
There is a one in two chance of drawing the fair coin. The chances of flipping heads again are 1 in 2. As a result, there is a 1 in 4 chance that the coin will land on heads.
There is a one in two chance of drawing the trick coin. The probability of flipping heads is then 2 to 1. As a result, there is a 2 in 4 chance that the coin will land on heads.
When each is multiplied by four, the resulting integers are
fair: 1 and trick: 2
and overall results: 3. (fair and tails is not counted)
The likelihood of a fair coin is one in three.
The likelihood that the chosen coin will show heads and be the fair coin is 33.333%.
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