Question

a sample of 38 people who recently hired an attorney yielded the following information about their attorneys.

\

$$\begin{tabular}{|c|c|} \\hline \\text{number of people} & \\text{would you recommend your attorney to a friend?} \\\\ \\hline 23 & \\text{yes} \\\\ \\hline 8 & \\text{no} \\\\ \\hline 7 & \\text{not sure} \\\\ \\hline \\end{tabular}$$

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.)

Explanation:

Identify the given values and target event

Using the Dependent Events knowledge point

• Total sample size \(N = 38\)
• Number of people who would not recommend ("No"): \(n_{\text{No}} = 8\)
• Number of people who are not sure ("Not sure"): \(n_{\text{Not sure}} = 7\)
• Target event: First person is "No", second person is "No", third person is "Not sure" (without replacement).

Calculate the probability of each sequential selection

Using the Dependent Events knowledge point

• First selection ("No"):

$$ P(\text{First No}) = \frac{8}{38} $$

• Second selection ("No" given first was "No"):

$$ P(\text{Second No} \mid \text{First No}) = \frac{7}{37} $$

• Third selection ("Not sure" given first two were "No"):

$$ P(\text{Third Not sure} \mid \text{First two No}) = \frac{7}{36} $$

Compute the joint probability

Using the Dependent Events knowledge point

$$ P(\text{No, No, Not sure}) = \frac{8}{38} \times \frac{7}{37} \times \frac{7}{36} $$

Simplify the resulting fraction

Using the Fraction Simplification knowledge point

$$
LATEXBLOCK0
$$

Answer:

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? <blank>\(\frac{49}{6327}\)</blank>