MDM4U Probability Using Counting Techniques
Worksheet
1. A person buys a ticket for a draw, which has tickets made up of four
digits from 0 to 9, and one winning ticket is drawn. Assuming that all
the tickets have been sold, determine the probability that the person wins
the draw.
2. The 7 members of a chess club line up for a picture. Determine the
probability that Mckenzie and Johann will be beside each other.
3. The letters of the word SIMILE are scrambled. Determine the
probability that the word is spelled exactly backwards.
4. A captain and co-captain for a fencing team are chosen from a hat
with the names of all 11 members in the hat. Determine the probability
that Lauren and Isabel are chosen as captain and co-captain respectively.
5. A health and safety committee is to be selected from all the people
who work at a local factory. The committee is to consist of four
members selected randomly from a list of ten names submitted by the
shop leader. The list has the names of five union members and five
workers who are not union members.
a) What is the probability that the first person selected from the list is a
union member?
b) What is the probability that the first two people selected are union
members?
c) What is the probability that all the committee members are union
members?
6. The 10 members of the Visual Arts council are seated for a
presentation. Determine the probability, in decimal form, that Julie and
Tamar will not be seated next to each other.
7. Five cards are dealt at random from a deck of 52 playing cards.
Determine the probability that you will have the 10 – J – Q – K – A of
the same suit.
8. A survey group of 5 students are chosen at random from 25
elementary students and 13 high school students. Determine the
probability that at least 2 of the students chosen are elementary students.
9. An airplane can make a safe landing if at least half of its engines are
working properly. Suppose that engine failures are independent events.
Determine whether the two-engine plane is safer than a four-engine
plane if the chance that the engine fails is 1 in 2. (Draw a tree diagram).
10. Suppose that a school’s female soccer team has a history of winning
50% of the games if it plays on rainy days and 60% of the games it plays
on fair days. The weather forecast for the next game day calls for an
80% chance of rain. What is the probability that the team will win the
game? Draw a tree diagram.
Answers
1. 0.00001
2.
3.
4.
2
7
1
360
1
110
1 2 1
5. , ,
2 9 42
6. 0.8
7.
1
649740
8. 0.96
3
11
4
16
9. Two-engine plane is safer: vs.
10. 0.52
.