Problem

A sample of 43 people who recently hired an attorney yielded the following information about their attorneys. \begin{tabular}{|c|c|} \hline Number of People & \begin{tabular}{c} Would You Recommend Your \\ Attorney to a Friend? \end{tabular} \\ \hline 23 & Yes \\ \hline 6 & No \\ \hline 14 & Not sure \\ \hline \end{tabular} Three people who provided information for the table were selected at random. Determine the probability that the first two would not recommend their attorney and the third is not sure if he or she would recommend their attorney. What is the probability that the first two would not recommend their attorney and the third is not sure if he or she would recommend their attorney? (Type an integer or a simplified fraction.)

Solution

Step 1 :The problem is asking for the probability of a specific sequence of events. The events are independent, meaning the outcome of one does not affect the outcome of the others. The total number of people is 43. The number of people who would not recommend their attorney is 6 and the number of people who are not sure is 14.

Step 2 :The probability of the first person not recommending their attorney is \(\frac{6}{43}\). After this person is selected, the total number of people is reduced to 42 and the number of people who would not recommend their attorney is reduced to 5. So, the probability of the second person not recommending their attorney is \(\frac{5}{42}\).

Step 3 :The total number of people is then reduced to 41 and the number of people who are not sure is still 14. So, the probability of the third person being not sure is \(\frac{14}{41}\).

Step 4 :The probability of all three events happening is the product of their individual probabilities. So, the final probability is \(\frac{6}{43} \times \frac{5}{42} \times \frac{14}{41} = 0.00567\).

Step 5 :Final Answer: The probability that the first two would not recommend their attorney and the third is not sure if he or she would recommend their attorney is approximately \(\boxed{0.00567}\).

From Solvely APP
Source: https://solvelyapp.com/problems/CNrKHvwLRJ/

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