Theory question 113
Probability(a) A man P has 5 red, 3 blue and 2 white buses. Another man Q has 3 red, 2 blue and 4 white buses. A bus owned by P is involved in an accident with a bus belonging to Q. Calculate the probability that the two buses are not of the same colour.
(b) A man travels from Nigeria to Ghana by air and from Ghana to Liberia by ship. He returns by the same means. He has 6 airlines and 4 shipping lines to choose from. In how many ways can he make his journey without using the same airline or shipping line twice?
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(a) P(same colour) = (5/10)(3/9) + (3/10)(2/9) + (2/10)(4/9) = (15 + 6 + 8)/90 = 29/90
P(not same colour) = 1 − 29/90 = 61/90
(b) Going: 6 airlines × 4 shipping lines; returning: 3 shipping lines × 5 airlines
Number of ways = 6 × 4 × 3 × 5 = 360
Find P(same colour) first and subtract from 1; on the return trip one airline and one shipping line are already used.