The multiplication rule for independent events. The probability that a randomly

Question

The multiplication rule for independent events. The probability that a randomly selected person prefers the vehicle color white is 0.24. Can you apply the multiplication rule for independent events in the situations described in parts (a) and (b)? If your answer is Yes, apply the rule. Two people are chosen at random from the population. What is the probability that both prefer white? Two people who are sisters are chosen. What is the probability that both prefer white? Write a short summary about the multiplication rule for independent events using your answers to parts (a) and (b) to illustrate the basic idea.

Explanation / Answer

a)

YES.

Hence,

P(both prefer white) = 0.24*0.24 = 0.0576 [ANSWER]

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b)

NO. We cannot apply the multiplication rule here.

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c)

From the two examples, we can see that we can only apply the multiplication rule if the two events are independent, that is, if the two events do not influence each other. As for the case of the sisters, it is probably that the choice of one sister influences the choice of the other, so we cannot apply the multiplication rule to them.

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