Respuesta :
Answer:
0.0076 = 0.76% probability that all five plants emerged from treated seeds
Step-by-step explanation:
The plants were 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:
6 + 6 = 12 seeds, which means that [tex]N = 12[/tex]
6 treated, which means that [tex]k = 6[/tex]
Five sprouted, which means that [tex]n = 5[/tex]
What is the probability that all five plants emerged from treated seeds?
This is P(X = 5). 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 = 5) = h(5,12,5,6) = \frac{C_{6,5}*C_{6,0}}{C_{12,5}} = 0.0076[/tex]
0.0076 = 0.76% probability that all five plants emerged from treated seeds
