A consumer organization estimates that over a 1-year period 17% of cars will nee

Question

A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired only once, 7% will need repairs exactly twice, and 4% will require three or more repairs. Suppose someone wanted to find certain probabilities regarding the number of repairs needed for the two cars they own. They use the Multiplication Rule to calculate these probabilities. Complete parts a) and b below. What must be true about their cars in order to make that approach valid? Repair needs for the two cars must be independent. The probability of repair needs for each car must be between 0 and 1 inclusive and the two probabilities must sum to 1. The consumer organization must have sampled all of the cars in the car owner's country when calculating the given percentages. Repair needs for the two cars must be disjoint. Is that assumption reasonable? Explain Choose the correct answer below No, because the sum of the probabilities of repair needs for each car may exceed 1. No, because the owner of the cars may treat both cars similarly. No, because it is generally impossible to sample an entire population. Yes, because reputable consumer organizations follow proper sampling techniques. Yes, because both cars needing repairs represents a probability of 1. Yes, because selecting one car guarantees that selecting the other car cannot happen. No, because repairing one car does not mean the other car will not need repairs. Yes, because there are probably a sufficiently large number of cars in the car owner's country that randomly selecting two cars can be considered two independent events.

Explanation / Answer

a) In order to apply the multiplication rule, repair needs for the two cars must be independent.

So option (A) is the correct choice.

b) The assumption is reasonable and option (H) is the correct choice.

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