Question

Two fair dice are rolled and the sum rolled is recorded.

a. Find the probability that the sum is 4. b. Find the probability that the sum is at least 4.

c. Find the probability that the sum is at most 4.

Answer 1

(A) total number of outcomes = 6*6 = 36

Finding P(sum is 4)

favourable outcome is events with a sum of 4 = 3 [(2,2),(3,1),(1,3)]

so, P(sum is 4) = favourable outcome/total outcome = 3/36 = 1/12 or 0.0833

(B) total number of outcomes = 6*6 = 36

Finding P(sum is at least 4)

favourable outcome is events with a sum at least 4 = 33 [all events except these three, i.e.(1,1),(2,1),(1,2)]

so, P(sum is at least 4) = favourable outcome/total outcome = 33/36 = 0.9167

(C) total number of outcomes = 6*6 = 36

Finding P(sum is at most 4)

favourable outcome is events with a sum at most 4 = 6 [(2,2),(3,1),(1,3),(1,1),(2,1),(1,2)]

so, P(sum is at most 4) = favourable outcome/total outcome = 6/36 = 1/6 or 0.1667