Problem 2. A study found that 70% of UTEP students have purchased books through

Question

Problem 2. A study found that 70% of UTEP students have purchased books through Amazon in the last semester. You ask five students if they have purchased books through Amazon in the last semester.

A)What is the expected number of students (out of five)?

B)What is the probability that none has purchased books through Amazon in the last semester?

C)What is the probability that all five have purchased books through Amazon in the last semester?

D)What is the probability that at least three has purchased books through Amazon in the last semester?

Explanation / Answer

p is 0.7 or 70%

the total number of students are 5

a) Expected value is n*p= 5*0.7=3.5

b) P(no one purchased)=(1-0.7)^5=0.00243

c) P(all 5 purchased)=(0.7)^5=0.16807

d) P(atleast 3 purchased)=P(x=3)+P(x=4)+P(x=5)= 5C3*(0.7^3)*(0.3^2)+5C4*(0.7^4)*(0.3^1)+(0.7)^5 = 0.83692

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