Respuesta :
Using the hypergeometric distribution, it is found that there is a 0.26 = 26% probability that the numbers on both balls are odd numbers.
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The balls are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes 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 successes.
- 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]
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In this question:
- 25 balls means that [tex]N = 25[/tex]
- From 1 to 25, there are 13 odd numbers, thus [tex]k = 13[/tex]
- 2 balls are chosen, which means that [tex]n = 2[/tex]
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The probability that the numbers on both balls are odd numbers is ?
This is P(X = 2). Thus
[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(2,25,2,13) = \frac{C_{13,2}*C_{12,0}}{C_{25,2}} = 0.26[/tex]
0.26 = 26% probability that the numbers on both balls are odd numbers.
A similar problem is given at https://brainly.com/question/24198127
