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. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

My Personal Notes arrow_drop_up
Article Tags :
Practice Tags :


3


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.