GATE CS 2025 Set 1 — Question 32
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Engineering Mathematics → Probability & Statistics → Bayes' Theorem
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Question
A box contains 5 coins: 4 regular coins and 1 fake coin. When a regular coin is tossed, the probability and for a fake coin, . 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)
Correct answer
0.49 to 0.51
Solution
Let be the event of picking a regular coin, and be the event of picking a fake coin.
Given:
Given:
- Total coins = 5
- Regular coins = 4
- Fake coins = 1
- For a regular coin, . Since tosses are independent:
- For a fake coin, :
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