MDM4U
1.2 Theoretical Probability
Learning Goals
I am learning to
• calculate theoretical probability
Investigate Outcomes and Events
1.
This table illustrates the possible outcomes when two standard dice are thrown.
a)
Complete the sum table on the right. Which sum(s) have the greatest theoretical probability?
What is the value of this probability?
b) Which sum(s) have the lowest probability? What is the value of this probability?
2.
What is the probability of rolling a 9 or greater?
3.  Reflect Explain how the table in this investigation was useful for calculating theoretical
probabilities.
4.  Extend Your Understanding Suppose 8-sided dice were used instead, numbered 1 through 8.
Would the theoretical probability of rolling each of the following sums increase, decrease, or
stay the same? Explain your answers.
a) 2
b) 9
c) doubles
Example 1 Calculate Theoretical Probability
Jake has 4 baseball jerseys (white, blue, grey and red) and 2 pairs of baseball pants
(white and grey).
a) Suppose he randomly picks a jersey and a pair of pants. Identify the sample
space for this experiment. HINT: You may make a list or tree diagram.
b) Jake does not want to wear the same colour jersey and pants. What is the
theoretical probability that he will randomly pick a uniform that is all one colour?
The Complement of an Event
Sometimes you need to know the probability that one event happens compared to all others. If one event is
A, then the event A' (read "A complement") is all of the possible outcomes not in A. This is known as the
complement of A.
Complementary Events
Because the sum of all probabilities in a sample space must equal 1, there is a useful relationship between
P(A) and P(A').
P(A) + P(A’) = 1
This relationship can be rearranged into two other useful forms.
P(A’) = 1 – P(A)
or
P(A) = 1 – P(A’)
Example 2 Probability of a Complement
In the game rock-paper-scissors, 2 opponents choose rock, paper or scissors using
hand gestures. Rock dulls scissors, scissors cut paper, paper covers rock.
a) What is the theoretical probability of a tie?
b) What is the probability of a win for either player (not a tie)?
Odds
One application of probability, often used in sports, is odds. Odds can be expressed as the odds in favour of
an event occurring or the odds against an event occurring. In sports it is actually more common to give the
odds against something happening.
The odds in favour of A = P(A) : P(A’)
The odds against A = P(A’) : P(A)
Example 3 Odds of an event
a) A hockey analyst gives the Canadian women’s hockey team a 75% probability of winning the gold
medal in the next Winter Olympics. Based on this prediction, what are the odds in favour of Canada
winning Olympic gold?
b) A local sports journalist estimates that the high school boys’ soccer team has a 40% probability of
going to the OFSAA championship tournament. What are the odds against the boys making OFSAA?
Consolidate and Debrief
R1. What is the theoretical probability of drawing a heart from a standard deck of cards?
R2. What is the complementary event to drawing a heart from a standard deck?
What is the theoretical probability of this happening?
Success Criteria
I will know I'm successful when I can
• apply tree diagrams to solve theoretical probability problems
• apply the complement of an event to calculate theoretical probability
Homework
p. 24, #1-4, 6, 7, 9, 10, 14
Errata:
Investigate
Q.1b Answer should say "2 or 12 have lowest probability"
Q. 2 Answer - should say P(9 or greater)
Q. 5 should include image of octahedral dice
Q. 5 Answers to parts (b) and (c) are wrong
No examples relating to Odds!
Note about Complement should come between Ex. 1 and Ex. 2
Consolidate and Debrief M/C question 4 refers to a spinner.
There is no spinner.