Using the hypergeometric distribution, it is found that there is a 0.0065 = 0.65% probability that both David and Valerie get picked for the Tahitian dance lesson.

The people are chosen without replacement from the sample, hence the <em>hypergeometric distribution </em>is used to solve this question.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

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

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

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

There is a total of 18 people, hence $N = 18$ .

2 people will be chosen, hence $n = 2$ .

David and Valerie corresponds to 2 people, hence $k = 2$ .

The probability that both get picked is P(X = 2), hence:

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

$P(X = 2) = h(2,18,2,2) = \frac{C_{2,2}C_{16,0}}{C_{18,2}} = 0.0065$

0.0065 = 0.65% probability that both David and Valerie get picked for the Tahitian dance lesson.

You can learn more about the hypergeometric distribution at brainly.com/question/25783392

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2 years ago