MDM4U Quiz (Ch. 7.1-7.2): Probability Distributions
Name: Jason Deng
Date: Jan 7 2022
Show ALL your work for full marks.
1. An 8-sided die has an equal chance of yielding a number from 1 to 8. If an even number
shows, you receive three times the value of the upper face in points. If an odd number shows,
you lose points equivalent to twice the value of the upper face.
(a) What is the probability that a number less than 6 will show when the die is rolled?
There is a 5/8 or 0.625 probability that a number less than 6 will appear. Numbers 1,2,3,4 and 5
come before 6.
[1 K]
Ans. = 5/8
(b) What is the expected value of this game?
1 (1/8) + 2 (1/8) + 3 (1/8) + 4 (1/8) + 5 (1/8) + 6 (1/8) + 7 (1/8) + 8 (1/8) = 4.5
[2 K]
Use expected value equation
Ans. Expected value is 4.5
2. A sailing club has eight 4.6 m boats, eleven 5.0 m boats, five 5.2 m boats, and five 6.1
m boats. These boats are assigned randomly to members who want to go sailing on
any given day.
(a) Make a table of the probability distribution for the length of an assigned boat.
[2 K]
Length, x
(m)
4.6
Probability,
P(x)
8/29
5.0
11/29
5.2
5/29
6.1
5/29
(b) What is the expected length of an assigned boat?
4.6 (8/29) + 5.0 (11/29) + 5.2 (5/29) + 6.1(5/29) = 5.11
[2 K]
Use expected value equation
Ans. Expected value is 5.11
3. A manufacturer produces 15% of its product with some defect. Four of these items are
selected randomly. What is the probability of at least two of them being defective?
Explain.
Find the probability of 0 and 1 being defective than subtract by 1 to find the probability
of at least 2 being defective.
n = 4 p =0.15 q = 1-0.15 = 0.85
X
0
1
P (X)
4C0 * 0.15^0 * 0.85^4 = 0.522
4C1 * 0.15^1 * 0.85^3 = 0.36
1 – (0.55+0.36) = 0.118
[2 C]
Ans. There is an 0.118 chance of at least 2 being defective
4. Prepare a table and a graph for a binomial probability distribution with n = 5 and p = 0.4
[5 C]