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Matt and Ryan are playing an exciting round of Rock Paper Scissors: The Collectible Card Game. Matt is convinced that Rock can beat anything, so his deck consists only of 8 Rock cards. Ryan's deck consists of 5 Paper cards and 3 Scissors cards. In the game, Matt randomly selects 3 cards from his deck and places them on the table. Ryan then randomly selects 3 cards and places one on each of Matt's cards. If Rock beats Scissors, Scissors beats Paper, and Paper beats Rock, then what's the probability that Ryan beats Matt in a landslide by choosing 3 Paper cards in a row?

Sagot :

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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