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Sagot :
Answer:
0.2384 = 23.84% probability that 3 were laser printers.
Step-by-step explanation:
The printers will be chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
20 orders means that [tex]N = 8[/tex]
8 were laser printers, which means that [tex]k = 8[/tex]
Sample of 5 means that [tex]n = 5[/tex]
What is the probability that 3 were laser printers?
This is P(X = 3).
[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(3,20,5,8) = \frac{C_{8,3}*C_{12,2}}{C_{20,5}} = 0.2384[/tex]
0.2384 = 23.84% probability that 3 were laser printers.
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