For each situation, identify the sample size n, the probability of success p, and the number of successes x. When asked for the probability, state the answer in the form b(n, p, x). There is no need to give the numerical value of the probability. Assume the conditions for a binomial experiment are satisfied.
a. According to Bloomberg Businessweek, 1 out of 10 students who take remedial courses in community college graduate within 3 years. In a random sample of 20 community college students who have taken remedial courses, what is the probability that exactly 6 will graduate within 3 years?
b. Fifty percent of students entering community colleges are put in at least one remedial class. If we randomly select 20 students entering community college, what is the probability that 6 are put in at least one remedial class?