Question

4. According to a household survey of Hong Kong in 2018, if an annual household income is over $25,000, the probability that the residents own 1 car is 15% and that of own 2 cars is 80%. Of the households surveyed, 60% had incomes over $25,000, 20% had 1 car and 70% had 2 cars. Assume that a household owns at most 2 cars in Hong Kong. Let X be the annual household income is over $25,000 and Ys be the residents own k cars, where k is the number of cars for k 0, 1 and 2. (a) Construct an appropriate diagram with the notation provided. (b) Find the probability that the residents of a household own 2 cars and have an income over $25,000 a year. (c) Find the probability that the residents of a household do not own 2 cars and have an income over $25,000 a year (d) Find the probability that the annual household income is over $25.000 if the do vosidants of a household have at least one car

Answer 1

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