For a certain musician, his favorite brand of guitar picks is far more likely to chip accidentally (and become useless) than to wear out. He drops by his local music shop to buy another one whenever his pick chips, on average 3 times a year. The shop has 4 picks in stock, in addition to the one he is using.
a) What are the average and standard deviation of the time (in months) until he goes to the shop and discovers they will have to order the pick he wants?
b) What is the probability that, 1.5 years from now, he will still have a usable pick without having had to order more?