Respuesta :
Answer:
0.5622 = 56.22% probability of getting no browns.
Step-by-step explanation:
The M&Ms 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:
13 + 5 + 10 + 8 + 8 + 4 = 48 total M&Ms, which means that [tex]N = 48[/tex]
Sample of 5 means that [tex]n = 5[/tex]
5 browns means that [tex]k = 5[/tex]
What is the probability of getting no browns?
This is P(X = 0).
[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 = 0) = h(0,48,5,5) = \frac{C_{5,0}*C_{43,5}}{C_{48,5}} = 0.5622[/tex]
0.5622 = 56.22% probability of getting no browns.
