Answer:
9/25 or 36%
Step-by-step explanation:
The probability of selecting the fair coin is 1/2, and the probability of getting heads with the fair coin is 1/2.
P(fair) = 1/2, P(heads | fair) = 1/2
The probability of selecting the unfair coin is 1/2, and the probability of getting heads with the unfair coin is 2/3.
P(unfair) = 1/2, P(heads | unfair) = 2/3
P(fair and 2 heads) = 1/2 (1/2)²
P(fair and 2 heads) = 1/8
P(2 heads) = 1/2 (1/2)² + 1/2 (2/3)²
P(2 heads) = 1/8 + 2/9
P(2 heads) = 25/72
Therefore, the probability that you selected the fair coin, given that you flipped 2 heads, is:
P(fair | 2 heads) = (1/8) / (25/72)
P(fair | 2 heads) = (1/8) (72/25)
P(fair | 2 heads) = 9/25
