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Puzzle 53 | The Counterfeit Coin

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A box contains n coins, of which 7 of them are counterfeit with tails on both sides and the rest are fair coins. If one coin is selected from the bag and tossed, the probability of getting a tail is 17/20. Find the value of ‘n’.         Answer: n = 10 Explanation: Probability of getting a tail can be in two ways 1) Selecting any of those 7 coins with tails on two side is = (7/n) 2) Selecting any one, other than those 7 biased coins is (n-7)/n Therefore:
(7/n)(1)        +     (n-7/n)*(1/2) = 17/20
|                                |
|                                |
|                                |
probability of          probability of
getting a tail from     getting a tail from
biased coins           fair coins 
solving above equation, we get n = 10 This Puzzle is contributed by Harika Mulumudi.

Last Updated : 18 Jan, 2023
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