Suppose there are 2 customers in the checkout line at Mario's Used Book Emporium. Each customer buys a number of books given by a random variable X with the following probability mass function.
| x |
1 |
2 |
3 |
4 |
| f(x) |
0.5 |
0.25 |
0.1 |
0.15 |
Further, the number of books purchased by any customer is independent of the number of books bought by any other customer.
a. What is the probability that (between the two customers currently in line) exactly 4 books are sold?
b. Now suppose there are 3 customers in line (and they independently buy books with the same probability distribution). What is the probability that (between these three customers) 5 or fewer books are sold?