In: Statistics and Probability
1. Compute the probability of no successes in a random sample of three items obtained from a population of 12 items that contains two successes. What are the expected number and standard deviation of the number of successes from the sample?
a) what is the expected number of the sample?
b) what is the standard deviation of the number of successes from the sample?
2. A professor of management has heard that 8 students in his class of 40 have landed an internship for the summer. Suppose he runs into three of his students in the corridor.
a) find the probability that none of these students has landed an internship.
b) find the probability that at least one of these students has landed an internship.