Peter throws two different dice together and finds the product . . .

Question : Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25?

Doubt by Pari

Solution : 

Case I : When Peter throws two different dice then total possible outcomes are 

{(1,1), (1,2), (1,3), (1,4), (1,5),
 (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)} = 36

No. of outcomes when product of the numbers on the two dice is 25 = {(5,5)} = 1

P(Getting 25) = 1/36 = 0.0278 ⋍ 0.028

Case II : Rina throws a die then total possible outcomes are
{1, 2, 3, 4, 5, 6} = 6

No. of outcomes when the square of the numbers on the two die is 25 
{5}=1

P'(Getting 25) = 1/6 = 0.1678⋍0.168

Clearly, P'(Getting 25)>P(Getting 25)

Hence, Rina has better chance to get the number 25.