# Compound probabilities

Compound probabilities involve the likeliness of two (or more) events occurring, e.g., rolling two dice.

## Free throws

Rule: A free throw allows a player to take two independent shots, each worth one point.

Steve Nash (90% per shot) - weighted tree diagram

• P(2 points)
• P(1 points)
• P(0 points)

Wilt Chamberlin (50% per shot) - weighted tree diagram

• P(2 points)
• P(1 points)
• P(0 points)

Professor Hlas (20% per shot) - weighted tree diagram and grid

• P(2 points)
• P(1 points)
• P(0 points)

## With or without replacement

Complete the following using a representation or your choice. It might be good to check your answer using another representation.

Q1. Two red marbles and two white marbles are in an opaque bag. A marble is drawn, replaced, then a second marble is drawn. What is the probability of drawing two red marbles?

Q2. Two red marbles and two white marbles are in an opaque bag. A marble is drawn, then a second marble is drawn. What is the probability of drawing two red marbles?

## Free Throws Challenge

A free-throw could result in 2 or 1 or 0 points. Find the "average points per free-throw" for each player.

Using the probabilities computed above, how many points would we expect each player to make given 100 free throws? On average, how many points would we expect for one free throw?