MDM 4U ~ Unit 1, Day 13
Mrs. Enns
UNIT 1 – ASSIGNMENT
NAME ________________________________
1. Suppose your school has the following numbers of students.
Grade
9
10
11
12
TOTALS
Male
113
109
85
115
422
Female
128
92
121
98
439
Totals
241
201
206
213
861
Determine the probability of each of the following events.
a. For a prize draw, the name of every student is placed in a hat. What is the
probability that the name of a male student in grade 11 will be chosen?
b. The grade 12 students are choosing a representative to sit on the Parent Council.
What is the probability that the representative will be female?
c. One male student and one female student will be chosen to ride on the school’s
float in the Thanksgiving Day parade. What is the probability that you will be
selected?
2. Two standard dice are rolled and the sum of each roll is recorded.
a. Create a tree diagram to represent all of the possible outcomes of rolling two dice.
b. What is the sample space for these dice?
c. What is n(S)?
d. What is the probability of each sum occurring?
e. Determine the sum of all of your answers in part d). Explain why this answer
turns out as it does.
f. What is the probability of rolling doubles with two dice?
3. A baseball player has had 14 hits in 60 times at bat in the last 20 games.
a. What is the probability that the player will get a hit the next time at bat?
b. What type of probability did you calculate in part a)?
c. How many hits does the batter need in her next ten at bats to increase the
probability of her getting a hit to 0.300?
4. Jenna has 17 computer games. Of these games, 5 are music related, 7 are simulations,
and 3 are both simulations and music related.
a. Create a Venn diagram to represent this situation.
b. Determine the probability that if Jenna randomly selects a game, the game is a
simulation but not music related.
c. Determine the probability that a game that Jenna selects will not be a simulation
or music related.
5. For each probability, determine the odds in favour.
a. 0.25
d. 1/7
b. 3/5
e. 35%
c. 60%
f. 0.001
6. In hockey, a team can win, lose, or tie any game. Assume that each outcome is equally
likely. A team plays a three-game series.
a. Create a tree diagram to represent the possible outcomes of the three games.
b. What are the odds in favour of the team winning all three games?
c. What are the odds in favour of the team winning the series by winning at least two
games?
d. What are the odds against the series ending in a draw (i.e., no distinct winner)?
7. In the film The Da Vinci Code, the main character must determine the correct word in a
five-letter cryptex. A cryptex in a kind of combination lock where five rings of 26 letters
must be rotated to spell a word. How many different arrangements of letters are
possible?
8. How many different five-digit even numbers can be made from the digits 2, 3, 4, 5, 6, and
9?
9. Phone numbers in Canada and the United States consist of a three-digit area code, a
three-digit exchange, and a four-digit number.
a. How many seven-digit phone numbers are possible if there are no restrictions?
b. How many three-digit exchanges are there if there are no restrictions?
c. If there are 210 exchanges in Ontario, what is the total possible number of sevendigit phone numbers?
d. If 11 area codes are in use in Ontario, what is the total possible number of tendigit phone numbers?
10. In each case, determine whether the expression is true or false.
a. 3! + 3! = 6!
b. (4 + 4)! = 8!
c. 5!6! = 30!
d. (15/3)! = 5!
11. A baseball team is lining up for a team photo. There are ten players and two coaches.
How many ways can they be arranged if
a. Everyone is in one line?
b. Everyone is in one line and the coaches are at each end?
12. Simplify.
a. (n + 2)!
n!
b. ( 2n )!
(2n – 2)!
13. For security, an e-mail program requires you to have a ten-character password and
change it every three weeks. You like your current password, XXQWERTYZZ, because
it is relatively easy to remember and type in. At the very least, you would like to keep
the same letters when you change your password. How many different passwords can be
created using your letters
a. With no restrictions?
b. Keeping QWERTY together?
c. Keeping QWERTY, the Zs, and the Xs together?
14. A class has 7 males and 21 females. How many ways can your teacher select four
students to go to the office to pick up boxes of textbooks if
a. There are no restrictions?
b. An equal number of males and females are selected?
c. The sample is stratified (i.e., the sample has the same proportion of members from
each group as the class has)?
d. If there is at least one female?
15. Consider the letters in the word MISSISSAUGA. How many different four-letter
arrangements can be made if
a. Each letter must be different?
b. There must be three Ss (e.g., SSSM)?
c. There are no restrictions?
16. Consider a standard deck of 52 playing cards.
a. How many ways are there to choose four cards?
b. What is the probability that all four cards you choose will be red?
c. What is the probability that all four cards you choose will be spades?