Probability Recap

Match the symbols with their appropriate meaning and usage.

• Union -- or

• U

• Intersection -- and

• |

• Given -- conditional

•  ∩

According to the two-way table, if we randomly-select a person, what is the probability that they prefer yoga? Write your answer as an unreduced fraction.

Mathematical Equivalence

ON

According to the two-way table, if we randomly-select a person, what is the probability that they prefer Swimming? Write your answer as an unreduced fraction.

Mathematical Equivalence

ON

Now, let's use our answers from the previous questions:

P(Yoga) = 35/150 and P(Swimming) = 40/150

Calculate P(Yoga U Swimming)

As you saw, U means or. We use the _________ rule to find these types of probabilities.

Now, let's use our answers from the previous questions:

P(Yoga) = 35/150 and P(Swimming) = 40/150

Calculate P(Yoga U Swimming)

Add the two probabilities together. Do NOT subtract yet.

Mathematical Equivalence

ON

Hopefully, you found the last answer to be 75/150 by adding the two together.

Are the events Yoga and Swimming mutually exclusive?

• Yes!

• No!

• What?

Answer explanation

Remember that mutually exclusive means the events CANNOT occur together. So, if two events are mutually exclusive, the probability of event 1 and event 2 happening at the same time is 0.

Hopefully, you found the last answer to be 75/150 by adding the two together.

Based on your answer to the last question, do we need to subtract any overlap?

• Yes!

• No!

• What?

Moving on!

Suppose we randomly-select an individual. Calculate P(Male ∩ Cycling). Remember, leave fractions unreduced!

Mathematical Equivalence

ON

Compute P(Running | Female)

Let's break this down. How many females are there in this survey?

Another way to think of it: What is the numerator of the probability of selecting a female?

Mathematical Equivalence

OFF

Compute P(Running | Female)

Hopefully, you got 90.

Now, out of those 90 people, how many prefer running?

In other words, how many females prefer running as their exercise?

Mathematical Equivalence

OFF