3333 % of college students say they use credit cards because of the rewards program. you randomly select 10 college students and ask each to name the reason he or she uses credit cards. find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, and (c) between two and five inclusive. if convenient, use technology to find the probabilities.

a. at r = 2

P = [10! / (10 - 2) ! 2!] * 0.33^2 * 0.67^ (10 - 2)

P = 0.1989 ~ 0.20 (answer)

b. We deduct the values of P when r = 0, r = 1, r = 2 from 1 to get all values when r > 2

at r = 0

P = [10! / (10 - 0) ! 0!] * 0.33^0 * 0.67^ (10 - 0)

P = 0.0182

at r = 1

P = [10! / (10 - 1) ! 1!] * 0.33^1 * 0.67^ (10 - 1)

P = 0.0898

so for r > 2, the probability is:

P = 1 - (0.1989 + 0.0182 + 0.0898)

P = 0.6931 (answer)

c. at r = 3

P = [10! / (10 - 3) ! 3!] * 0.33^3 * 0.67^ (10 - 3)

P = 0.2614

at r = 4

P = [10! / (10 - 4) ! 4!] * 0.33^4 * 0.67^ (10 - 4)

P = 0.2253

at r = 5

P = [10! / (10 - 5) ! 5!] * 0.33^5 * 0.67^ (10 - 5)

P = 0.1332

So when r is between 2 and 5 inclusive, the probability is:

P = 0.1989 + 0.2614 + 0.2253 + 0.1332

P = 0.8188 (answer)