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?
A
137/216
B
17/36
C
173/216
D
5/6
Correct Option - A
Explaination
definitely higher.
36+36+36 = 108 ways
If she scores 1,
Eric's score will always be greater.
If she scores 4,
her score will be higher only if Eric scores (1,1), (1,2) or (2,1)
3 ways
If she scores 9,
Eric's score will be greater if he scores (3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), (6,5), (6,6)
Eric's score will be lesser in (36-10 =)26 ways.
n(E) = 108+0+3+26
= 137
n(S) = No. of ways of throwing three dice
= 6*6*6 = 216
P(E) = 137/216