Question

Use the table in the following table, which lists survey results from high school drivers at least 16 years of age. Assume that subjects are randomly selected from those included in the table.

Answer 1

Using the hypergeometric distribution, it is found that:

The probability that four randomly selected high school drivers all drove when drinking alcohol is 0.000145.

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• The students are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

In this distribution, the probability of exactly x successes is:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:  

• N is the size of the population.
• n is the size of the sample.
• k is the total number of desired outcomes.

Combination formula:  

$C_{n,x} = \frac{n!}{x!(n-x)!}$

• Total of $709 + 2966 + 179 + 4232 = 8086$ students, thus $N = 8086$.
• 709 + 179 = 888 drove while drinking, thus $k = 888$
• 4 students are selected, thus $n = 4$.
• The probability that all four drank is: P(X = 4).

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 4) = h(4,8086,4,888) = \frac{C_{888,4}*C_{7198,0}}{C_{8086,4}} = 0.000145$

Thus, the probability is of 0.000145.

A similar problem is given at https://brainly.com/question/4818951