Carcass wrote:
The integers 1 through 5 are written on each of five cards. The cards are shuffled and one card is drawn at random. That card is then replaced, the cards are shuffled again and another card is drawn at random. This procedure is repeated one more time (for a total of three times). What is the probability that the sum of the numbers on the three cards drawn was between 13 and 15, inclusive?
Express your answer as a fraction.
Total ways to withdraw these 3 cards = \(5^3 = 125\)
Sum as 13 = 355, 535, 553, 445, 454, 544
Sum as 14 = 455, 545, 554
Sum as 15 = 555
Required probability = \(\frac{10}{125} = \frac{2}{25}\)