Mary and Jenna are playing a game in which each girl rolls a twenty-sided die with numbers from 1 to 20 on the faces. If the number on the die that Mary rolls is a factor of the number on the die that Jenna rolls, Mary wins. If the number on the die that Jenna rolls is a factor of the number on the die that Mary rolls, Jenna wins. For how many possible rolls would both girls win?

Question

Jakob Holland

Mathematics

20 September, 04:29

Mary and Jenna are playing a game in which each girl rolls a twenty-sided die with numbers from 1 to 20 on the faces. If the number on the die that Mary rolls is a factor of the number on the die that Jenna rolls, Mary wins. If the number on the die that Jenna rolls is a factor of the number on the die that Mary rolls, Jenna wins. For how many possible rolls would both girls win?

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Joshua Lynch · Answer 1

Both girls would win 1/20 of the time. Since there is not a set number of rolls given, we cannot estimate that.

The only way that both girls can win is if they roll the same number. The only numbers that are both factors of each other would have to be the same number. There are 20 ways of the girls rolling the same number, out of a sample space of 20 (20) = 400. 20/400 = 1/20