jmc

Question

Ten tiles numbered 1 through 10 are turned face down. One tile is turned up at random, and a die is rolled. What is the probability that the product of the numbers on the tile and the die will be a square?

Accepted Answer

The numbers can at most multiply to be 60. The squares less than 60 are 1,4,9,16,25,36, and 49. The possible pairs are (1,1),(1,4),(2,2),(4,1),(3,3),(9,1),(4,4),(8,2),(5,5),(6,6), and (9,4). There are 11 choices and 60 possibilities giving a probability of 1160.