2929% 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,

The binomial distribution can be used to model the given situation because:
1. The experiment is Bernoulli, i.e. with exactly two outcomes (because of rewards program or not)
2. Probability is known (29%) and remains constant throughout the experiment
3. The number of trials is known and not variable (10)
4. Sampling is assumed random (given) and independent(assumed from context).

The probability of selecting x successes (because of rewards program) from a sample of size n=10 with probability p (=0.29) is given by the binomial distribution as:
P(x,n,p)=C(n,x)*(p^x)*(1-p)^(n-x)
where C(n,x) is the number of combinations of x object from n, given by C(n,x)=n!/(x!(n-x)!)

(a) Probability that exactly two students say they use credit cards because of the rewards program
P(X=2)
=P(2,10,0.29)
=C(10,2)*(0.29^2)(0.71^8)
=0.244

(b) Probability that MORE than two students say they use credit cards because of the rewards program
P(X>2)
=1-P(X<=2)
=1-(P(X=0)+P(X=1)+P(X=2))
=1-P(0,10,0.29)+P(1,10,0.29)+P(2,10,0.29))
=1-(C(10,0)*(0.29^0)(0.71^10)+C(10,1)*(0.29^1)(0.71^9)+C(10,2)*(0.29^2)(0.71^8))
=1-(0.033+0.133+0.244)
=1-0.410
=0.590

Yes, that is the correct formula. to solve this problem given the number of years, plug in the number of years for t and plug the whole thing into the