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

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: multiply exponents per exponent rules to get: remember you subtract exponents from the denominator and add exponents in the numerator so: simplify further: so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.