GATE 2025 CS (CS1) – Question 32
A box contains 5 coins: 4 regular coins and 1 fake coin. When a regular coin is tossed, the probability $P(head) = 0.5$ and for a fake coin, $P(head) = 1$. You pick a coin at random and toss it twice, and get two heads. The probability that the coin you have chosen is the fake coin is _______. (rounded off to two decimal places)
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Correct answer: 0.50
Explanation
P(fake and HH) = (1/5)(1) = 0.2. P(regular and HH) = (4/5)(1/4) = 0.2. The posterior is 0.2/0.4 = 0.50.