Puzzle 53 | The Counterfeit Coin

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.