Question

Two dice are thrown simultaneously .the probability that the product of the numbers appearing on the top faces of the dice is a perfect square

Answer 1

possible outcome of throwing two dice simultaneously= 36
product of 2 outcome having product a perfect square: (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)
favourable outcome = 6
probability= 6/36
= 1/6

Answer 2

The probability of getting a square number as product of number on top faces is 2/9

1) Rolling a dice gives 6 possible outcomes.

2) Rolling 2 dice gives 6*6 = 36 possible outcomes.

3) The favorable outcome is that product of the numbers equal a square number.

4) Possible square numbers are : 1,4,9,16,25,36

5) Total Ways to form 1 is 1 = 1,1

Total Ways to form 4 is 3 =  1,4     2,2      4,1

Total Ways to form 9 is 1 =   3,3

Total Ways to form 16 is 1 = 4,4

Total Ways to form 25 is 1 = 5,5

Total Ways to form 36 is 1 = 6,6

6) Hence the total favorable outcomes are :-8

7) The probability would be = 8/36 = 2/9