A marketing firm is considering making up to three new hires. Given its specific needs, the management feels that there is a 60% chance of hiring at least two candidates. There is only a 5% chance that it will not make any hires and a 10% chance that it will make all three hires.
a. What is the probability that the firm will make at least one hire?
b. Find the expected value and the standard deviation of the number of hires.