Question

a sample of 36 people who recently hired an attorney yielded the following information about their attorneys.

three people who provided information for the table were selected at random. determine the probability that they would all recommend their attorneys.

what is the probability that the three people would all recommend their attorneys?

(type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the probability of the first person recommending

The total number of people is \(22 + 4+10=36\). The number of people who would recommend is \(22\). So the probability that the first - person recommends is \(P_1=\frac{22}{36}\).

Step2: Calculate the probability of the second person recommending

After one person is selected (who recommended), there are \(36 - 1=35\) people left, and \(22-1 = 21\) people who would recommend. So the probability that the second - person recommends is \(P_2=\frac{21}{35}\).

Step3: Calculate the probability of the third person recommending

After two people are selected (who recommended), there are \(35 - 1=34\) people left, and \(21-1 = 20\) people who would recommend. So the probability that the third - person recommends is \(P_3=\frac{20}{34}\).

Step4: Calculate the combined probability

Since these are independent events (in the sense of sequential selection without replacement), the probability that all three recommend is \(P = P_1\times P_2\times P_3\).

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Answer:

\(\frac{11}{51}\)