Respuesta :
Answer:
0.2333 = 23.33% probability that both of them have the secret decoder ring
Step-by-step explanation:
The cereals 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]
In this question:
45 boxes, which means that [tex]N = 45[/tex]
22 have the secret decoder ring, which means that [tex]k = 22[/tex]
Two boxes, which means that [tex]n = 2[/tex]
What is the probability that both of them have the secret decoder ring?
This is P(X = 2). So
[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(2,45,2,22) = \frac{C_{22,2}*C_{23,0}}{C_{45,2}} = 0.2333[/tex]
0.2333 = 23.33% probability that both of them have the secret decoder ring
