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MDM 4UI
Discrete Probability Distributions
Probability Distributions – Group Study Activity
In groups of 2, 3 or 4 solve the following permutation problems. Write full solutions
and check your answers against the key provided.
1. At the Toyota plant in Cambridge, an assembly line robot installs CD players
in each car produced on the line. For quality control, the units are tested to
make sure they are installed properly. The robot has a probability of
malfunctioning of 0.2.
a) Determine the probability distribution of the number of tests
performed before a malfunction is found. (Only complete the
distribution for 0.2 ! P ! 0.09)
b) What is the expected number of tests before a malfunction is found?
2. A school lottery has 5000 tickets for sale. There is one grand prize of $2000
and five second prizes of $100.
a) Determine the expected value of this lottery and interpret what it
represents.
b) If you buy a ticket for $1, what is your expected value?
c) How can the school use the expected value to help determine the
ticket price?
3. A bag contains six red marbles, five yellow marbles and four black marbles.
Marbles are selected from the bag, one at a time, without replacement until
four marbles have been taken.
a) Determine the probability distribution for choosing red marbles.
b) Determine the expected number of red marbles.
4. Conner has five shots in a shoot-out competition. Historically, Conner has a
probability of 35% (a very high probability) of scoring on a shoot-out.
a) Assuming this probability stays constant, create a table showing the
probability distribution and the expected number of goals Conner
might score.
b) What is the probability of Conner scoring more than two goals?
c) What is the expected number of goals Conner will score?
Answer key
1b) 4
4c) 1.75
2a) $0.50
2b) – $0.50
3b) 1.6
4b) 23.4%
MDM 4UI
Unit 4 – Discrete Probability Distributions
SELF QUIZ
1. The eighteenth hole at a public golf course is a par 4. This means that a good golfer
should be able to play the hole in 4 strokes. The table below summarizes the scores of
golfers who recently played the hole.
Number of
Strokes, x
1
Frequency
Probability, P(x)
x * P(x)
0
2
3
3
24
4
45
5
51
6
38
7
24
8
9
E(x) =
a) Complete the Probability Distribution chart for the number of strokes above.
b) What is the expected value for the number of strokes a golfer will take on this hole? _________
c) Is it reasonable that the expected value for the hole should differ from the par value? Explain.
2. The Nestle Candy Company manufactures Smarties, a candy coated chocolate. On
average, 40% of all Smarties are red. For the Hallowe’en sized boxes, the production line
mixes the candies randomly and packages ten per box.
a)
What is the probability that less than four candies in a given box are red?
b)
What is the probability that at least four candies in a given box are red?
c) What is the expected number of red candies per box?
3. For a symmetrical eight-sided die,
a) what is the probability that it will take exactly two tries to roll a 7?
b) what is the expected waiting time until a 7 is rolled?