Filter
Top Products
Exercises
1. Find 13!
2. Find the number of ways to deal a five-card hand from a deck of 52 cards.
3. Find the number of four-digit numbers that don’t have any digits repeated.
4. A company has 50 fork-lifts. On any given day each fork-lift has a 1% chance of needing
maintenance. What is the probability that today 3 forklifts will need maintenance?
5. For the same company, what is the probability that at most 5 trucks will need maintenance
today?
6. A small store has on the average 23 customers per day. Using a Poisson distribution as a
model, find the probability that the store will have 20 customers today.
7. For the same store, what is the probability that they will have more than 21 customers
today?
8. Use a geometric distribution to find the probability that it will take 3 rolls to roll a 5.
9. Find the probability that it will take at most 4 rolls to roll a 5.
Solutions
1. 6,227,020,800
2. Since we don’t care about the order of the cards, we want the number of ways of selecting
5 objecsts from 52, ie., 52C5 = 2,598,960.
3. Since we do care about the order of the digits, we want the number of permutations of four
objects chosen from 10, ie., 10P4 = 5040
4. This is a binomial distribution with n = 50, p = 0.01, and the probability is binompdf (50,
0.01, 3) = 1.2%.
5. We want a cumulative binomial probability. Binomcdf (50, 0.01, 5) = 99.999%
6. poissonpdf (23,20) = 7.2%
7. This is a cumulative probability problem. The complement of having more than 21
customers is having at most 21 customers, which has probability poissoncdf (23, 21) =
38.9%. The probability of having more than 21 customers is 100% - 38.9% = 61.1%
8. The probability of rolling a 5 is 1/6. We want geometpdf (1/6, 3) = 11.6%.
9. We want a cumulative probability: geometcdf (1/6, 4) = 51.8%.
38