Using the hypergeometric distribution, there is a 0.1786 = 17.86% probability that Ryan beats Matt in a landslide by choosing 3 Paper cards in a row.
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.
For this problem, we have that Ryan will win if he takes 3 Paper cards from a set of 8(5 paper and 3 scissors), hence the parameters are given as follows:
N = 8, k = 5, n = 3, x = 3.
Hence the probability is given by:
[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 = 3) = h(3,8,3,5) = \frac{C_{5,3}C_{3,0}}{C_{8,3}} = 0.1786[/tex]
0.1786 = 17.86% probability that Ryan beats Matt in a landslide by choosing 3 Paper cards in a row.
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
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