You are doing laundry, and you are trying to find any small new red socks which may have fallen into the pile of white clothes in the laundry basket by mistake. It's really dark in your basement laundry room, so you have to randomly sample items of clothing.
a. In a single laundry basket, there are 35 white socks and 10 red socks. If you sample 5 socks at random (without replacement), what is the probability that at least one of them will be a red sock?
b. Now suppose instead of being in your basement laundry room, you are dealing with this problem at a huge cotton clothing manufacturer's pre-wash room, where there are 35,000 white socks and 1000 red socks. You sample 5 items of clothing at one time. What is the approximate probability at least one of them will be a red sock?
c. Using your answer to part b, how many 5-item samples of clothing would you expect to have to take to find the first 5-item sample with at least one red sock?