Question 991297: the probability of getting the product a perfect (square of a natural numbers) when two dice are thrown together,is
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the perfect squares are:
1*1 = 1
2*2 = 4
3*3 = 9
4*4 = 16
5*5 = 25
6*6 = 36
the number of possible products when you throw 2 dice is equal to 6 * 6 = 36
they are:
1*1 = 1 ***
1*2 = 2
1*3 = 3
1*4 = 4 ***
1*5 = 5
1*6 = 6
2*1 = 2
2*2 = 4 ***
2*3 = 6
2*4 = 8
2*5 = 10
2*6 = 12
3*1 = 3
3*2 = 6
3*3 = 9 ***
3*4 = 12
3*5 = 15
3*6 = 18
4*1 = 4 ***
4*2 = 8
4*3 = 12
4*4 = 16 ***
4*5 = 20
4*6 = 24
5*1 = 5
5*2 = 10
5*3 = 15
5*4 = 20
5*5 = 25 ***
5*6 = 30
6*1 = 6
6*2 = 12
6*3 = 18
6*4 = 24
6*5 = 30
6*6 = 36 ***
out of these only 8 generate a perfect square.
the probbility of getting a perfect square is therefore 8/36 = 4/18 = 2/9.
note that there are more possible factors of two number that equal a perfect square, but the highest factor has to be less than or equal to 6 which is the maximum number possible on one 6 sided die.
for example:
16 = 1*16 or 2*8 ot 4*4 or 8*2 or 16*1
out of all these factors, only 1 is possible, which is 4*4.
the only one where all possible factors can be considered is 4.
4 is the product of 1*4 or 2*2 or 4*1.
all these factors are possible when you are throwing 2 die.
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