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 hypergeometric distribution is used to solve this question.
What is the hypergeometric distribution formula?
The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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 [tex]N = 18[/tex].
- 2 people will be chosen, hence [tex]n = 2[/tex].
- David and Valerie corresponds to 2 people, hence [tex]k = 2[/tex].
The probability that both get picked is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,18,2,2) = \frac{C_{2,2}C_{16,0}}{C_{18,2}} = 0.0065[/tex]
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 https://brainly.com/question/25783392
