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Sagot :
The probability that the balls have the same number is 0.001094 = 0.1094%.
The probability can be calculated using the hypergeometric distribution, a discrete probability distribution that calculates the likelihood an event occurs k times in n trials when you are sampling from a small population without replacement.
Hypergeometric distribution is used because the balls are chosen without replacement.
Hypergeometric distribution formula:
P (X = x) = h (x, N, n, k) = [tex]\frac{Ck,xCN-k,n-x}{CN,n}[/tex]
with parameters as follows:
x = the number of successes.
N = the size of the population.
n = the size of the sample.
k = the total number of desired outcomes.
In this case, we have given data:
There are 40 balls, so N = 40.
For each number, there are 4 balls, so k = 4.
4 balls are selected, hence n = 4.
For each ball, the probability is P (X = 4). There are 10 balls, so we have to find 10P (X = 4).
P (X = x) = h (x, N, n, k) = [tex]\frac{Ck,xCN-k,n-x}{CN,n}[/tex]
P (X = 4) = h (4, 40, 4, 4) = [tex]\frac{C4,4C26,0}{C40,4}[/tex] = 0.0001094
0.0001094 x 10 = 0.001094
Hence, 0.001094 = 0.1094% is the probability that the balls have the same number.
Learn more about probability at: https://brainly.com/question/11234923
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