Probability Scenarios and Tree Diagrams

This lesson explores the use of tree diagrams to represent sample spaces and calculate probabilities. It includes examples such as primary color combinations, game outcomes over two nights, and birth outcomes in families. The lesson demonstrates how tree diagrams can visually display all possible outcomes and assist in computing probabilities.

What is the primary purpose of using a tree diagram in probability?

• To predict future events

• To eliminate unlikely outcomes

• To calculate the average of outcomes

• To list all possible outcomes in a concise manner

In the family game night scenario, what does the outcome 'CB' represent?

• Two consecutive nights of card games

• A board game on the first night and a card game on the second night

• A card game on the first night and a board game on the second night

• Two consecutive nights of board games

What is the probability of playing a board game on both nights in the family game night scenario?

• 56.25%

• 25%

• 75%

• 18.75%

How is the probability of an outcome determined in a tree diagram?

• By multiplying the probabilities of each stage

• By adding the probabilities of each stage

• By subtracting the probabilities of each stage

• By dividing the probabilities of each stage

In the two-child family scenario, what is the probability of having two girls?

• 12.5%

• 75%

• 25%

• 50%

What is the probability of having exactly one girl in the two-child family scenario?

• 12.5%

• 25%

• 75%

• 50%

In the two-child family scenario, which outcome represents having one boy and one girl?

• BB

• GG

• BG or GB

• BB or GG

What is the probability of having two boys in the two-child family scenario?

• 12.5%

• 75%

• 25%

• 50%

How does the probability of having two girls compare to having exactly one girl in the two-child family scenario?

• Greater than

• Less than

• Equal to

• Not comparable

What is the total probability of all possible outcomes in a tree diagram?

• 0.25

• 0.5

• 2

• 1