Pre Calculus
Name:________________________________________
Unit 1: Probability Homework
Standard 1a: Determine the permutations of a set
1. The Cash it in Lottery requires that you choose 5 different numbers from 1-30. How many different lottery
tickets can you create?
2. A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible
combinations of pizza with three toppings are there (you can repeat toppings)?
3. How many ways can 5 paintings be lined up on a wall?
4. A lock has four dials. On each dial are the digits 0 to 9.
a. How many possible combinations are there if you can repeat digits?
b. How many possible combinations are there, if no digit can repeat?
5. Which of the following gives the number of ways to arrange the letters in Ghandi?
A. 5!
B. 6!
C.
D.
6!
2!
6!
6!5!4!3!2!1!
6. How many distinct ways can you to arrange the letters in pineapple?
7. How many 2-digit numbers can you make using the digits 1, 2, 3 and 4 without repeating the digits?
8. A president, vice president, and treasurer must be elected from a group of 12 students. How many ways can
the positions be assigned?
9. Describe why 0! Equals 1.
Standard 1b: Apply combinations formula
10. How many different 13- card hands include the ace and king of spades?
11. A restaurant offers a platter of 1, 2, or 3 appetizers. If they offer 5 different types of appetizers how many
ways are there to order the platter?
12. A 3-person committee is elected from a 25 member group of women. Is this an example of a combination or
a permutation? Explain.
13. Expand the binomial (3𝑥 + 𝑦)4 .
14. Create a binomial whose third term has a leading coefficient of 15.
15. Determine the 𝑎5 term in the expansion of (2𝑎 − 𝑏)48 .
Standard 1c: Determine the probability of an event
16. If a die is thrown, what is the probability that it will show a 3 or a multiple of 2?
17. A card is picked from a deck then put back into the deck then a card is drawn again. What is the probability
the same card is drawn twice?
18. A lock has four dials. On each dial are the digits 0 to 9.
a. What is the probability of not having a 4 in the combination if digits can repeat?
b. What is the probability of not having a 4 in the combination if digits cannot repeat?
19. You have a deck of regular playing cards and draw 4 cards, what is the probability you will draw at least
one face card.
20. You roll a dice 3 times, what is the probability you will roll at least one 3?
21. Determine if the events A and B below are overlapping or disjoint (mutually exclusive).
a. Event A: a number is greater than 3
Event B: a number is even.
b. Event A: a person is a senior
Event B: a person is in kindergarten.
c. Event A: a candy bar has nuts
Event B: a candy bar has caramel.
22.
Number of scoops of
ice cream Lauren will
buy
Probability
0
1
2
0.02
0.55
0.43
Number of scoops
of ice cream Betsy
will buy
Probability
State the following probabilities.
a. Lauren and Betsy both buy 2 scoops of ice cream.
b. Lauren and Betsy collectively buy at least one scoop of ice cream.
0
1
2
0.015
0.6
0.54
23. The probability that it rains on Jonah’s birthday is 0.7. The probability that it rains on Frankie’s birthday is
0.85. State the following probabilities:
a. It rains on both Frankie and Jonah’s birthdays.
b. It rains on Frankie’s birthday, but not Jonah’s birthday.
c. It rains on Jonah’s birthday but not Frankie’s birthday.
d. It rains on exactly one person’s birthday. Either Frankie or Jonah, but not both.
e. It rains on either Frankie or Jonah’s birthday.
24. A bag has 10 tiles with each number from 1-10 listed on one chip. What is the probability of reaching in and
grabbing an even number then an odd number without replacement?
25. Given a class of 30 students with 12 females and 18 males. 7 students are chosen at random to attend a
conference.
a. What is the probability that all males are chosen to go to the conference?
b. What is the probability that at least one female is chosen to go to the conference?
Standard 1d: Use conditional probability to determine the probability of dependent events
26. When you arrive home today you find 27 cupcakes on a plate. There are 13 with icing, 11 have sprinkles, 4
have both, and some are plain. Draw a Venn diagram to represent this situation then use it to answer the
probabilities below:
a. What is the probability you randomly chose a cupcake with icing?
b. What is the probability you randomly chose a cupcake with sprinkles?
c. What is the probability you randomly chose a cupcake with sprinkles, given it has icing?
27. A group of students were surveyed as to their political affiliation and the type of ice cream they prefer. The
results are below. Fill in the blanks in the table then answer the questions.
a. What is the probability that a randomly selected person likes Strawberry ice cream given that the person
is Independent?
b. What is the probability that a randomly selected person is Independent given that the person likes
strawberry ice cream?
28. Two boxes are on the table. One box contains a normal coin and a two headed coin, the other box contains
three normal coins. A friend reaches in a box and removes a coin and shows you one side: a head. What is
the probability that the coin came from the box with the two-headed coin?
Standard 1e: Calculate the expected value of an event.
29. A raffle is held by a student association to draw for a $1000 plasma television. Two thousand tickets are
sold at $1.00 each. Fill in the table and find the expected value of one ticket.
Outcome
Probability
Expected Value: __________
30. Assume a person pays $1 to play the following game. Four coins are tossed. If all coins show the same
(all heads or all tails), the player wins $6; otherwise, the player loses. Find the expected value for this
game and describe what it means.
31. A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll
of a red loses. A roll of green pays $2.00. The charge to play the game is $2.00. How much would a roll
of blue have to pay for the expected value of the game to equal $1.50?