Understanding The Problem
The key to solving the problem is understanding that it takes very little time to collect the first few coupons. On the other hand, it takes a long time to collect the last few coupons. In fact, for 50 coupons, it takes on average 50 trials to collect the very last coupon after the other 49 coupons have been collected. This is why the expected time to collect all coupons is much longer than 50. The idea now is to split the total time into 50 intervals where the expected time can be calculated.
Read more about this topic: Coupon Collector's Problem
Famous quotes containing the words understanding the and/or problem:
“Awareness of the stars and their light pervades the Koran, which reflects the brightness of the heavenly bodies in many verses. The blossoming of mathematics and astronomy was a natural consequence of this awareness. Understanding the cosmos and the movements of the stars means understanding the marvels created by Allah. There would be no persecuted Galileo in Islam, because Islam, unlike Christianity, did not force people to believe in a “fixed” heaven.”
—Fatima Mernissi, Moroccan sociologist. Islam and Democracy, ch. 9, Addison-Wesley Publishing Co. (Trans. 1992)
“My problem lies in reconciling my gross habits with my net income.”
—Errol Flynn (1909–1959)