Answered

consider the following binomial experiment. the probability that a green jelly bean is chosen at random from a large package of jelly beans is 1/4. if sally chooses 12 jelly beans, what is the probability that at most two will be green jelly beans? a) 0.4137 b) 0.6500 c) 0.3907 d) 0.6093 e) 0.5000 f) none of the above.

Sagot :

The probability that at most two of the chosen beans will be green jelly beans is 0.39.

The possibility of choosing a green jelly bean at random from a large package of jelly beans is = 1/4 = 0.25

So, p = 0.25

The possibility that the chosen bean at random from a large package of jelly beans is not a green jelly bean will be  = 1 - 0.25

So, q = 0.75

The sample size is 12.

So, n = 12

We have to find the probability that at most 2 of the chosen beans will be green jelly beans. This means that the green beans can be 0, 1, or 2.

The formula used to find probability in binomial distribution is:

P (r) = C (n,r) × [tex]p^{r}[/tex] × [tex]q^{n-r}[/tex]

To find the probability that at most two of the chosen beans will be green jelly we will find the sum of P(0), P(1), P(2).

So, the required probability is,

= P(0) + P(1) + P(2)

= C (12,0) × [tex]0.25^{0}[/tex] × [tex]0.75^{12}[/tex] +  C (12,1) × [tex]0.25^{1}[/tex] × [tex]0.75^{11}[/tex] + C (12,2) × [tex]0.25^{2}[/tex] × [tex]0.75^{10}[/tex]

= 0.031 + 0.127 + 0.232

= 0.39

To know more about probability here.https://brainly.com/question/28380809#

           

#SPJ4