Question
A box consists of 125 apples out of which 25 are rotten.
Khushboo comes to buy non-rotten apple. The shopkeeper takes out two apples and hands it over to Khushboo one after another. If the apple is not rotten she buys else the shopkeeper keeps them back. What is the probability that Khushboo buys at least one apple?Solution
Case I: Khushboo buys two apples
Probability of buying first apple = (125 - 25)/125 = 100/125 = 4/5
Probability of buying second apple = (100 - 1)/(125 - 1) = 99/124
∴ Probability of buying two apples = (4/5) X (99/124) = 99/155
Case II: Khushboo buys one apple
Probability that she is offered non-rotten apple in first attempt and rotten in second = 100/125 X 25/124 = 5/31
Probability that she is offered rotten apple in first attempt and non - rotten in second = 25/125 X 100/125 = 4/25
∴ Required Probability = 99/155 + 5/31 + 4/25 = 24/25
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