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Meyer rolls two fair, ordinary dice with the numbers $1,2,3,4,5,6$ on their sides. What is the probability that both dice show a square number?

 Nov 12, 2021
 #1
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Of the numbers:  1, 2, 3, 4, 5, 6,  the two square numbers are  1  and  4

 

The probability that the first die shows a square number is  2 / 6.

The probability that the second die shows a square number is also  2 / 6.

 

The probability that both show a square number is (2/6) x (2/ 6)  =  

 Nov 12, 2021
 #2
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Even though there are 2 dice, but they are tossed ONCE simultabeously as follows:

 

(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) ,  Total == 36

 

Therefore, there are only 2 possibilities of tossing 2 squares: (1, 4) and (4,1): The probability is 2 / 36 ==1/18

 Nov 12, 2021
 #4
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OOps.... you listed the other two possibilities, but didn't count them   4 4   and   1 1

Guest Nov 12, 2021
 #3
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6 x 6 = 36 possible rolls

 

two squares rolls include   1 1    1 4     4 1   and 4 4

4 out of 36      = 1/9

 Nov 12, 2021

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