Answer:
P(S=k) = (1/35)k
8/21
Step-by-step explanation:
P(S=k) is proportional to k
P(S=k) = ck
Total probability is 1
k = 2,3.... 8
Sum of all probabilities =
2c + 3c + 4c + 5c + 6c + 7c + 8c = 1
35c = 1
c = 1/35
P(S=k) = (1/35)k, where k = 2,3,...8
P(1&1):
P(S=2) = 2/35
P(2&2):
P(S=4)/3 = (1/3)(4/35) = 4/105
Because for S=4: (1,3) (2,2) (3,1) and all are equally likely
P(3&3):
P(S=6)/3 = (1/3)(6/35) = 2/35
Because for S=6: (2,4) (3,3) (4,2)
P(4&4):
P(S=8) = 8/35
P(getting doubles = 2/35 + 4/105 + 2/35 + 8/35 = 40/105 = 8/21
