The multiplication rule for independent events. The probability that a randomly
ID: 3130384 • Letter: T
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 to illustrate the basic idea.Explanation / Answer
Note that the multiplication rule is for independent events only, that is, 2 events that do not influence each other.
a)
YES, WE CAN APPLY IT, as it is a random sample.
Hence, if both prefer white,
P = 0.24*0.24 = 0.0576 [ANSWER]
*******************
b)
NO, WE CANNOT APPLY IT, as they have some relationship.
********************
c)
Note that we can apply the multiplication rule for independent events only, that is, 2 events that do not influence each other. If two events are independent, then the probability of them happening together is the product of their probabilities.