Theory question 110
Probability(a) A pair of fair dice each numbered 1 to 6 is tossed. Find the probability of getting a sum of at least 9, (b) If the probability that a civil servant owns a car is 1/6, find the probability that: (i) two civil servants, A and B, selected at random, each owns a car, (ii) of two civil servants, C and D selected at random, only one owns a car, (iii) of three civil servants, X, Y and Z, selected at random, only one owns a car.
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(a) Outcomes with sum ≥ 9: (3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), (6,5), (6,6) = 10 of 36.
P = 10/36 = 5/18.
(b)(i) 1/6 × 1/6 = 1/36.
(ii) P(C only) + P(D only) = 2 × 1/6 × 5/6 = 10/36 = 5/18.
(iii) 3 × 1/6 × 5/6 × 5/6 = 75/216 = 25/72.
'Only one' means one owns a car AND the others do not: multiply by 5/6 for each non-owner.