Question

A bag contains 100 apples, 100 bananas, 100 oranges, and 100 pears. if i pick one piece of fruit out f the bag every minute, how long will it be before i am assured of having picked at least a dozen pieces of fruit of the same kind?

Answer 1

Suppose you withdrawn 11 fruits of same kind, say apple. The worst case to withdrawn the fruit of same kind would be 11 more fruits of same kind but not apple, say bananas. Now going through your worst luck, you will again get 11 fruits of same kind, say Oranges. Now you have 11 apples, 11 bnanas, 11 oranges, none of which making a dozen of same kind of fruit. In that situation, if you get either an apple, or a banana or an orange, you will get dozen pieces of same kind of fruit. But your luck is so bad, that you got 11 pears. You've got 44 fruits, none of which is the same kind making a dozen. Now even if you withdraw any fruit, you will make a dozen fruit of same kind. Hence you've to take atleast 45 fruits to be sure that you've taken out a dozen of same kind of fruit.

45 is the answer.