MDM4U – FINAL Problem Set
Part 1: Select 2 of the following 4 questions to complete. I am only looking for the right answer
here. No need to work out a full solution (Total of 2 marks)
1. Calculate the number of 4-digit numbers you can make with the number 0-9. For all
questions all numbers are positive (i.e., there are no negative numbers).
a) Repetition is not allowed.
b) The 2nd digit is 5 and the number is even, repetition is allowed.
2. Calculate the following:
(15¿ )¿ ¿¿ 67!
a) ¿ b) 63!
3. If 5 cards are dealt from a standard deck of 52, answer the following questions:
a) How many hands don’t have a face card?
b) How many hands will have exactly 2 cards of one suit and 3 cards of another suit?
4. A civil jury of 12 members must be selected from 12 males and 13 females.
a) In how many ways can a jury of 12 people be selected from the group?
b) In how many ways can the jury of at least 1 woman be selected from the same group?
Part 2: Select 1 question write the solution in the organizer provided below. DO NOT STATE
Assumptions. (3 marks each)
1. A bag contains Lego blocks. 3 are red, 5 are blue, and 4 are yellow. 2 Lego blocks are drawn
without replacement. What is the probability of drawing a red block, given that the first block
was yellow?
2. 12 girls and 19 boys (total 31 people) are running for 6 positions on the school’s Graduation
Committee. 3 of the 12 girls are sisters, and each candidate is equally likely chosen. Calculate the
following: What is the probability that Meg must be on the committee, or it must be an all-girls
committee?
Part 3: Full worked out solution:
Use the solution organizer provided below.
Select 1 of the following questions to answer with full solutions ( 5 marks)
1) Many people believe that high school students are OBSESSED with their cell phones, especially
while in Data Management class. If the probability that the teacher will catch a student using their
3
cell phone is 5 . What is the probability the teacher will catch students using their cell phones at least
3 days?
2. There are 6 birds and 8 hamsters in a pet store. Five pets are chosen at random to be relocated to
a different store. What is the expected number of birds to be sent to the other store?
3. Homer really wants to stop working at the nuclear power plant. He buys some lottery tickets
from the local Kiwiki-Mart. The probability of winning on a ticket is 4 in 20. What is the
probability Homer will win on his third ticket?
Part 4:
Select 1 of the following 3 Normal Distribution questions to answer with full solution (Select 1
of the following question) ( 5 marks)
1. The lifetime the common house cat ranges uniformly from 10 to 16 years. Determine the
probability that a cat selected at random will live less than 11.5 years.
2. 10% of North Americans have blue eyes. There are 850 students at Ancaster High School. What
is the probability that exactly 95 of these students have blue eyes?
3. A biologist measures the body length of 100 Japanese sardines. Their lengths are normally
distributed, with a mean of 20.20 cm and a standard deviation of 1.65 cm.
What is the probability that a sardine’s length will be between 19.0 and 21.0 cm long?
Part 5: Communication: Write your solution in the organizer below (5 marks)
Consider a game in which you roll a regular eight-sided die. When you roll an odd number, you
win an amount of money equal to double the roll. When you roll an even number, you lose an
amount of money equal to half the roll.
a) What is the expected value of the money received? Is this a fair game? Why or why not?
b) Draw a probability distribution histogram for this situation
Solution Organizer
Part 1:
Answer: Place your answers in the box below. 1 mark each for right answer ( 2 marks)
ANS:
ANS:
Part 2
Answer: Place your answers in the box below. Solution (3 marks= 1 mark for plugging correct
numbers, 1 mark for right answer, 1 mark for conclusion statement)
ANS:
Part 3: Discrete Probability functions and distribution (total 5 marks)
State one specific assumption that you will State the type of distribution you are working
use for this question (1 mark) with
Solution (3 marks):
1 mark for using correct formulae
1 mark for plugging in correct numbers into formulae
1 mark for correct answer
Part 4: Normal Distribution (total 5 marks)
Define the Random Variable X and
state the mean and standard State the probability formula (0.5)
deviation (1 mark)
Convert the probability formula as a function of
z-score(0.5)
Solution (3 marks)
1 mark for converting to proper z-score to a probability.
1 mark for using the correct formula.
1 mark for right answer.
Part 5: Communication Answer: (5 marks)
1 mark for calculating the expected value:
2 marks for stating whether it is a fair game and mark for explaining why or why not
2 marks for Probability Histogram
ANS:
Probability Histogram of Dice game:
Total: - 20 marks
