Question

Eric throws two dice, and his score is the sum of the values shown. sandra throws one die, and her score is the square of the value shown. what is the probability that sandra's score will be strictly higher than eric's score?

Answer 1

Law of total probability:
W be the event that Sandra's score is strictly higher than Eric's score.
Sample space for Sandrs's score = S =  {1, 4, 9, 16, 25, 36}.    

P(W)=+ +P(W∣S=1)P(S=1)+P(W∣S=4)P(S=4)P(W∣S=9)P(S=9)+P(W∣S=16)P(S=16)P(W∣S=25)P(S=25)+P(W∣S=36)P(S=36)=16(0+336+2636+1+1+1)=137216