Probability Recap

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.

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.

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 (a)   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.

Moving on!

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

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?

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?

Hopefully, you got 20.

Let's put it altogether! Suppose we randomly-select an individual. What is the probability that they prefer running, given that they are a female?

Are the events "Swimming" and "Male" Independent?

Let's find out. Let A = Swimming and B = Male

Here is the general rule for independence, which we will break down: P(A) = P(A|B) = P(A|B^C)

What is the probability of randomly-selecting an individual who prefers swimming?

Are the events "Swimming" and "Male" Independent?

Let's find out. Let A = Swimming and B = Male

Here is the general rule for independence, which we will break down: P(A) = P(A|B) = P(A|B^C)

Write that last fraction down so you don't forget.

What is the probability of randomly-selecting someone who prefers swimming, given that they are male?

Are the events "Swimming" and "Male" Independent?

Let's find out. Let A = Swimming and B = Male

Here is the general rule for independence, which we will break down: P(A) = P(A|B) = P(A|B^C)

Write that last fraction down so you don't forget.

What is the probability of randomly-selecting someone who prefers swimming, given they are NOT male? (HINT: What category in this table is not male?)

Let's put those fractions together that you hopefully got:

40/150 = 15/60 = 25/90

Determine if that statement is true. Then, complete the sentence by dragging the correct terms.

Since these fractions ​ ​ (a)   equal, the events ​ (b)   and​ (c)   are not​ (d)   .