Probability+problems

Worksheet: Probability Problems

Multiple Choice
Identify the choice that best completes the statement or answers the question.

____ 1. A group of volleyball players consists of four grade-11 students and six grade-12 students. If six players are
chosen at random to start a match, what is the probability that three will be from each grade?
a. b. c. d.

____ 2. If a bowl contains ten hazelnuts and eight almonds, what is the probability that four nuts randomly selected
from the bowl will all be hazelnuts?
a. b. c. d.

____ 3. Without looking, Jenny randomly selects two socks from a drawer containing four blue, three white, and five
black socks, none of which are paired up. What is the probability that she chooses two socks of the same col-
our?
a. b. c. d.

____ 4. A euchre deck has 24 cards: the 9, 10, jack, queen, king, and ace of each suit. If you were to deal out five
cards from this deck, what is the probability that they will be a 10, jack, queen, king, and ace all from the
same suit?
a. b. c. d.

____ 5. A bag contains 26 tiles, each marked with a different letter of the alphabet. What is the probability of being
able to spell the word math with four randomly selected tiles that are taken from the bag all at the same time?
a. b. c. d.

Short Answer

6. Participants in marathons are often given numbers to wear, so that race officials can identify individual run-
ners more easily. If the numbers are assigned randomly, what is the probability that the eight fastest runners
will finish in the order of their assigned numbers, assuming that there are no ties?
7. A club with eight members from grade 11 and five members from grade 12 is to elect a president, vice-presid-
ent, and secretary. What is the probability (as a percentage to one decimal place) that grade 12 students will be
elected for all three positions, assuming that all club members have an equal chance of being elected?
8. A four-member curling team is randomly chosen from six grade-11 students and nine grade-12 students. What
is the probability that the team has at least one grade-11 student?
9. If a CD player is programmed to play the CD tracks in random order, what is the probability that it will play
six songs from a CD in order from your favourite to your least favourite?
10. What is the probability that at least two people in a class of 30 students have the same birthday? Assume that
no one in the class was born on February 29.

Problem

11. Suppose you randomly draw two marbles, without replacement, from a bag containing six green, four red, and
three black marbles.

a) Draw a tree diagram to illustrate all possible outcomes of this draw.
b) Determine the probability that both marbles are red.
c) Determine the probability that you pick at least one green marble.
12. A six-member working group to plan a student common room is to be selected from five teachers and nine
students. If the working group is randomly selected, what is the probability that it will include at least two
teachers?
13. Len just wrote a multiple-choice test with 15 questions, each having four choices. Len is sure that he got ex-
actly 9 of the first 12 questions correct, but he guessed randomly on the last 3 questions. What is the probabil-
ity that he will get at least 80% on the test?
14. Leela has five white and six grey huskies in her kennel. If a wilderness expedition chooses a team of six sled
dogs at random from Leela’s kennel, what is the probability the team will consist of
a) all white huskies?
b) all grey huskies?
c) three of each colour?

15. Six friends go to their favourite restaurant, which has ten entrees on the menu. If the friends are equally likely
to pick any of the entrees, what is the probability that at least two of them will order the same one?

Worksheet: Probability Problems
Answer Section

MULTIPLE CHOICE

1. ANS: C PTS: 1 REF: Knowledge & Understanding
OBJ: Section 6.3 TOP: Calculating probability
2. ANS: B PTS: 1 REF: Knowledge & Understanding
3. ANS: B PTS: 1 REF: Knowledge & Understanding
4. ANS: D PTS: 1 REF: Knowledge & Understanding
5. ANS: C PTS: 1 REF: Knowledge & Understanding

SHORT ANSWER

6. ANS:

PTS: 1 REF: Applications OBJ: Section 6.3 TOP: Calculating probability
7. ANS:
3.5%

8. ANS:
about 0.9077

9. ANS:

or about 0.001 39

10. ANS:
about 0.7063


PROBLEM

11. ANS:
a)

b)

c)

12. ANS:

13. ANS:

A score of 80% requires getting 12 out of the 15 questions right. If Len answered 9 out of the first 12 ques-
tions correctly, he can score 80% only if he guessed all 3 of the remaining questions correctly.

Therefore Len has only about a 1.6% chance of getting 80% on the test.

14. ANS:
a) The probability is 0 since there are only 5 white huskies available.

b) Since there are 11 dogs altogether, the team can be chosen in ways. However, there are only 6 grey
huskies, so there is only one way of picking an all grey team. The probability of randomly selecting this
team from the 11 dogs is

c)

15. ANS:
This question is similar to the birthday problem in Example 3 on p.323 of the student textbook.

If none of the friends pick the same entree, there are ways to select their meals. The probability of this
event is

Therefore, the probability that at least two will order the same entree is 1 – 0.1512 = 0.8488, or about 84.9%.


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