Download Chapter 4 Review

MDM 4U
Chapter 4 _ Probability Review
1. A media class of 25 students randomly selects 3 of its students to be the news anchor, sports reporter, and weather
person by pulling names out of a hat. Explain whether a permutation or combination should be used to determine the
number of ways that a selection can be made and why.
2. Explain why subtraction is not involved in the determination of the number of elements in the union of two disjoint sets.
3. It is said that a sports team can gain confidence if it wins games and can lose confidence if it loses games. Explain
how the formula for conditional probability applies when determining the probability of a team winning its next two
games, given that it has a 50% chance of winning the first game. State what this probability must be greater than
given this theory of confidence.
4. Prove that C(n + 4, r + 1) = C(n + 3, r + 1) + C(n + 3, r).
5. Larry and Curly decide to have a chess match. The odds against Larry are 3:2. Each time Larry wins, he gains
confidence and the probability of winning the next game increases by 0.1. Each time he loses, his confidence goes
down and his probability of winning the next game decreases by 0.05. Determine the probability that in a three game
match Larry wins at least two games.
6. In a class of 33 students, 22 take geography, 24 take science, 20 take french, 17 take geography and science, 17 take
science and french, 13 take geography and french, and 12 take all 3 courses. Determine the probability that if a
student is selected at random, the student does not take any of these 3 courses.
7. Kirk's Convenience store sells 15 different brands of chocolate bars. Of these, 6 brands contain nuts, 5 brands contain
caramel, and the rest are pure milk chocolate. If 8 chocolate bars are to be purchased, determine the number of ways
they can be purchased so that at least 2 of them contain nuts.
8. Two students are chosen at random from a group consisting of 5 girls and 3 boys. Determine the probability that both
students are girls given that at least one is a girl.
9. A game is played by choosing two cards randomly from a deck of cards. Every time you choose two cards that are
face cards or two cards that are consecutive (i.e. 4 and 5, Jack and Queen), you win the game. If you receive $2.00
every time you win the game, determine the expected amount of winnings after 50 games.
10. Determine the probability that when a pair of dice is rolled that a sum of eight or doubles occurs. Show all work and
use the addition principle for probabilities.
11. A game consists of tossing a coin, cutting a deck of cards, and rolling a die. Bonus points are given if you repeat
exactly the outcomes of your previous turn. Determine the probability on your first turn that you have tails, an ace,
and an even number on the die, and then you receive bonus points in the next two turns.
12. A music-store bin contains 6 CDs, 7 DVDs, and 9 posters. If you randomly choose 3, one at a time, without
replacement, determine the probability that you choose a DVD, then a poster, and then another DVD.
13. A students' council with 22 members must select 3 students to help run a fundraiser. This is to done by randomly
selecting 3 names from the 22 names available. The council has 3 students from grade 9, 4 students from grade 10, 10
students from grade 11, and the remainder from grade 12. Determine the probability that 2 out of the 3 names are
chosen from the same grade.
14. A card is chosen from a deck of cards and a coin is tossed. Design an experiment using a spinner to determine the
probability of drawing a heart and tossing tails. Explain why a spinner would not be practical when the probability of
drawing the ace of spades and hearts is to be determined.
15. A group of students was surveyed to determine if they owned a racing bike or a mountain bike. Out of the 43 students
surveyed, 12 indicated they owned a racing bike, 33 indicated they owned a mountain bike, and 6 said they owned
both. Determine the probability that, if a student were to win a bike in a school raffle, it would be the first racing or
mountain bike.
MDM 4U
16. Find
if P(n, 3) = 3n
C(n
2, 2).
17. A box contains balls with the numbers 1 to 40 on it. One ball is drawn randomly. The probability of choosing a
number divisible by 3 is to be determined. State the value of
.
18. A jar of marbles contains 40% black marbles, 30% red marbles, 10% yellow marbles, and the remainder are green
marbles. If a marble is drawn randomly, determine the probability that it is yellow if is known that it is not green.
19. Two dice, one red and one green are rolled. What is the probability that the total will be an odd number given that a
number less than four was rolled on the red die?
20.
State the number of ways that the 9 members of the debating club can be lined up for a picture if Frasier must be on
the far left and Samantha and Charlotte must be together.
21. A bag contains 3 green blocks, 5 purple blocks, and 6 red blocks. If four blocks are drawn one at a time, without
replacement, determine the probability that the order is red, red, purple, green.
22. The letters of the word INFINITY are scrambled. Determine the probability that F is the first letter and Y is the last
letter.
23. Four identical chocolate bars, three identical bags of chips, and 6 identical popsicles are lined up on a prize table.
Determine the number of ways that this could be done.