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# probability help

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A pair of standard six-sided die are rolled. The probability that the digits rolled can be arranged to form a two-digit perfect square is

(A) 1/9 (B) 2/9 (C) 7/36 (D) 1/4 (E) 1/3

Nov 10, 2021
edited by Guest  Nov 10, 2021

#1
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A pair of standard six-sided die are rolled. The probability that the digits rolled can be arranged to form a two-digit perfect square is

(A) 1/9 (B) 2/9 (C) 7/36 (D) 1/4 (E) 1/3

The 2-digit perfect squares that can be made are 16, 25, 36, 64

1,1   1,2   1,3   1,4   1,5   1,6

2,1   2,2   2,3   2,4   2,5   2,6

3,1   3,2   3,3   3,4   3,5   3,6

4,1   4,2   4,3   4,4   4,5   4,6

5,1   5,2   5,3   5,4   5,5   5,6

6,1   6,2   6,3   6,4   6,5   6,6

So there are eight rolls that will give you the necessary digits, out of thirty-six possible rolls.

8/36  =  2/9  so the answer is (B).

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Nov 10, 2021
#2
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The probability is (A) 1/9.

Nov 10, 2021
#3
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The problem says the digits can be rearranged, so there are twice as many as you counted.

Guest Nov 10, 2021
#5
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If you're the guest who gave the wrong answer, if you had explained how you got that answer, you might have realized that you were overlooking one condition of the problem, that the digits the dice represent could be rearranged.

Guest Nov 10, 2021
edited by Guest  Nov 10, 2021