Respuesta :
Answer:
0.000002089 probability of winning this prize
Step-by-step explanation:
After a number is chosen, it cannot be chosen again. So we use the hypergeometric distribution 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:
53 numbers, then N = 53.
7 numbers picked, so n = 7.
Total of desired outcomes(any number which the player picks is desired) is 7, so k = 7.
6 successes, so x = 6.
What is the probability of winning this prize?
[tex]P(X = 6) = h(6,53,7,7) = \frac{C_{7,6}*C_{46,1}}{C_{53,7}} = 0.000002089[/tex]
0.000002089 probability of winning this prize
