Question

3131​% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is​

(a) exactly​ three,
(b) at least​ four, and​
(c) at most two.
If​ convenient, use technology to find the probabilities.

Answer 1

a) 0.23235

b) 0.53806

c) 0.22959

Explanation:

Given-

Adults having cashews as their favorite kind of nut
`= 0.31`

Adults not having cashews as their favorite kind of nut
`= 1-0.31\\= 0.69`

a) Exactly three

`(12)/(3) * (0.31)^3* (0.69)^9\\= 0.23235`

Thus, the probability that three adults have cashews as are their favorite nut is​ 0.23235

b) at least​ four

`1-P(1)-P(2)-P(3)\\`

`1-[({(12)/(1) * (0.31)^1* (0.69)^(11))+({(12)/(2) * (0.31)^2* (0.69)^(10))+({(12)/(3) * (0.31)^3* (0.69)^(9))]`

`=0.53806`

c) at most two

`({(12)/(1) * (0.31)^1* (0.69)^(11))+({(12)/(2) * (0.31)^2* (0.69)^(10))\\= 0.22959`