Please Help, I'm stuck (3)

Question

Janica throws one dice.

The value is recorded as "A"

She then rolls another two dices.

The product of the 2 values is recorded as "B"

If B < A, she rolls another 3 dices.

The sum of the 3 values is recorded as "C"

If C<B, she wins.

Otherwise, she loses.

Find the probability of her winning and losing.

Answer 1

 

 A={1,2,3,4,5,6}

 

B={1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,36}

 

 

C={3,4,5,6,7,8,9,10,...,18}

 

Prob(B<A) = 12/18 = 2/3

Prob (C<B) = 16/24 = 2/3

 

12/18 * 16/24 = 2/3*2/3 = 4/9