Question

Ten tiles numbered 11 through 1010 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

Answer 1

11/60

Explanation:

The numbers on the tiles are 1 through 10.

The numbers on the die are 1 through 6.

Products of a number on a tile and a number on the die range from 1 × 1 = 1 to 10 × 6 = 60.

All squares from 1 to 60 are:

1, 4, 9, 16, 25, 36, 49

There are 60 possible products of tile number and die numbers.

The combinations that result in a square are, in order (Tile, Die):

(1, 1), (1, 4)

(2, 2)

(3, 3)

(4, 1), (4, 4)

(5, 5)

(6, 6)

(8, 2)

(9, 1), (9, 4)

There are 11 outcomes out of 60 that are squares.

p(product = square) = 11/60

Answer: 11/60