SOLUTION: A box contains 10 chits of which 3 chits are eligible for a prize. A boy named Kathan randomly selects two chits from this box. Find the probability that Kathan gets the prize.

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Question 1200342: A box contains 10 chits of which 3 chits are eligible for a prize. A boy named Kathan randomly selects two chits from this box. Find the probability that Kathan gets the prize.
Answer by ikleyn(52835) About Me  (Show Source):
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A box contains 10 chits of which 3 chits are eligible for a prize.
A boy named Kathan randomly selects two chits from this box.
Find the probability that Kathan gets the prize.
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The box containins two categories of chits: 

        (a) 3 Good for a prize,  
    and 
        (b) 7 Bad for a prize.


The total number of pairs to take at a time from 10 shits is

    C%5B10%5D%5E2 = %2810%2A9%29%2F2 = 45.


The total number of pairs BAD for the prize is

    C%5B7%5D%5E2 = %287%2A6%29%2F2 = 21.


The rest of the pairs, 45 - 21 = 24, will win a prize.


Therefore, the probability to win a prize is  P = 24%2F45 = 8%2F15.    ANSWER

Solved, with full explanation.

Learn the logic of this solution. It is used in million other similar problems.