Question 755569
In a recent survey eighteen percent of high school students said their favorite cookie was macadamia-white chocolate. You randomly select 4 students and ask each person to name their favorite cookie. Find the probability that the number who say macadamia-white chocolate is their favorite cookie is:

X~Binomial(4,0.18)

A) exactly 2

P(X = 2) = {{{(matrix(2,1,4,2))(0.18^2)(0.82^2)}}} = {{{highlight(0.1307)}}}


B) less than 3

P(X < 3) = {{{sum((matrix(2,1,4,x))(0.18^x)(0.82^(4 - x)), x = 0, 2)}}} = {{{highlight(0.9798)}}}

C) at least 3

P(X &#8805; 3)  = 1 - 0.9798 = {{{highlight(0.0202)}}}

D) greater than 1
P(X > 1) = {{{sum((matrix(2,1,4,x))(0.18^x)(0.82^(4 - x)), x = 2, 4)}}} = {{{highlight(0.1509)}}}

E) at most 2

P(X &#8804; 2) = {{{sum((matrix(2,1,4,x))(0.18^x)(0.82^(4 - x)), x = 0, 2)}}} = {{{highlight(0.9798)}}}