AP Sec 5.3 Conditional Probability

AP Sec 5.3 Conditional Probability

Independence and the Multiplication Rule

Conditional Probability

Fill in the Blanks

Find P(S|T) = P(survived|third-class passenger) =

Fill in the Blanks

Find P(died|not third-class passenger) =

Calculating Conditional Probabilities

Open Ended

A survey of all residents in a large apartment complex reveals that 68% use Facebook, 28% use Instagram, and 25% do both. Write those three things using probability notation.

Fill in the Blanks

If P(F) = 0.68, and P(I) = .28, and P(F and I) = 0.25 what is the probability a resident uses Facebook given they have an Instagram account?

P(Facebook|Instagram)

AP Exam Tip

You can use notation like P(A|B) if the events are defined in the problem. Otherwise, it's probably easier to use contextual labels like P(Instagram|Facebook) or P(I|F).

Independent Events IF:

• P(A|B) equals

• P(Anot B) equals

• P(A)

Poll

Is being a female independent of being right-handed?

• Yes, independent

• No, not independent

• Hmmm... is this a trick question?

Open Ended

To check for independence between two events check P(R|F) and P(R|not F) and P(R). Are being female and right-handed independent events? Show evidence for your response.

General Multiplication Rule

Fill in the Blanks

P(A) = 0.79 and P(B) = 0.39 and they are independent events.

Find P(A and B).

RECALL: P(A and B) = P(A) * P(B|A)

Fill in the Blanks

P(A) = 0.79 and P(B) = 0.39 and they are independent events.

Find P(A or B)

RECALL: P(A or B) = P(A) + P(B) - P(A and B)

Learning Targets

• Conditional probability... P(A|B)=P(AandB)/P(B)

• Independence is when...P(A)=P(A|B)=P(A|B')

• General Multiplication rule...P(AandB)=P(A)*P(B|A)