1. Fundamentals of Probability
Unit 7A
Fundamentals of Probability
Ms. Young

2. Definitions
Outcomes are the most basic possible results of observations or experiments.
An event consists of one or more outcomes that share a property of interest.
Ms. Young

3. Expressing Probability
The probability of an event, expressed as P(event), is always between 0 and 1 (inclusive).
A probability of 0 means the event is impossible and a probability of 1 means the event is certain. 1
0.5
Certain
Likely
Unlikely
50-50 Chance
Impossible
0 ≤ P(A) ≤ 1
Meteorology offers a rich source of ideas here. Would you take an umbrella to work if the chance for rain is at 10%? How about 90%?
Ms. Young

4. Theoretical Method for Equally Likely Outcomes
Step 1: Count the total number of possible outcomes.
Step 2: Among all the possible outcomes, count the number of ways the event of interest, A, can occur.
Step 3: Determine the probability, P(A).
Ms. Young

5. Outcomes and Events
Assuming equal chance of having a boy or girl at birth, what is the probability of having two girls and two boys in a family of four children?
Of the 16 possible outcomes, 6 have the event two girls and two boys.
P(2 girls) = 6/16 = 0.357
One of the challenges many students have with probability is knowing when to trust intuition and when to back away from it. Many students would answer the question with a 50%. This problem is a classic example of the importance of looking at the total number of outcomes.
Ms. Young

6. Empirical and Subjective Probabilities
An empirical probability is based on observations or experiments. It is the relative frequency of the event of interest.
A subjective probability is an estimate based on experience or intuition.
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7. Three Types of Probabilities
Theoretical probability
The chance of
rolling a 4 is 1 out of 6.
Empirical probability
Subjective probability
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8. Three Types of Probabilities
Theoretical probability
She’s a 92% free throw
shooter for the season.
Empirical probability
Subjective probability
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9. Three Types of Probabilities
Theoretical probability
There’s about a 70%
chance she will go out
on a date with me.
Empirical probability
Subjective probability
Ms. Young

10. Probability of an Event Not Occurring
If the probability of an event A is P(A), then the probability that event A does not occur is 1 – P(A).
Since the probability of a family of four children having two girls and two boys is 0.375, what is the probability of a family of four children not having two girls and two boys?
P(not 2 girls) = 1 – = 0.625
Ms. Young

11. Making a Probability Distribution
A probability distribution represents the
probabilities of all possible events. To make a
probability distribution, do the following:
Step 1: List all possible outcomes. Use a table or figure if it is helpful.
Step 2: Identify outcomes that represent the same event and determine the probability of each event.
Step 3: Make a table listing each event and probability.
Ms. Young

12. A Probability Distribution
All possible outcomes and a probability distribution for the sum when two dice are rolled are shown below.
Possible outcomes
Point out that the reason 7 is considered a lucky number in many gambling games is simply because there are more ways to roll a 7 than any other number.
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13. Odds
Odds are the ratio of the probability that a particular event will occur to the probability that it will not occur.
The odds for an event A are
The odds against an event A are
Ms. Young