Gr 11 Math Ch 10: Tree Diagrams

What does each level of a tree diagram represent?

A stage in the sequence of events (correct)

The product of probabilities of multiple events

Different outcomes of an event

Independent events

What is the formula for the probability of multiple independent events occurring?

P(A) - P(B)

P(A) / P(B)

P(A) + P(B)

P(A) × P(B) (correct)

What is the purpose of a tree diagram?

To organize and visualize the different possible outcomes of a sequence of events (correct)

To calculate the probability of a single event

To determine the probability of dependent events

To calculate the sum of probabilities of multiple paths

What is the probability of a path in a tree diagram?

The product of the probabilities along that path Signup and view all the answers

What is the formula for the probability of dependent events?

P(A) × P(B|A) Signup and view all the answers

How do you calculate the probability of multiple paths leading to a desired outcome?

Sum the probabilities of each path Signup and view all the answers

What is represented on each branch of a tree diagram?

The probability of a specific event Signup and view all the answers

What is the first step in drawing a tree diagram?

Represent the outcomes of the first event Signup and view all the answers

What is the probability of multiple events occurring when the events are dependent?

The product of the probability of the first event and the conditional probabilities of the subsequent events Signup and view all the answers

What do you need to do to calculate the probability of a specific sequence of events in a tree diagram?

Follow the path from the start to the end point and multiply the probabilities Signup and view all the answers

Why are tree diagrams useful?

To organise and visualise the different possible outcomes of a sequence of events Signup and view all the answers

How do you draw a tree diagram for a sequence of events?

By representing the outcomes of the first event first Signup and view all the answers

What is the probability of an event if there are multiple paths leading to that event?

The sum of the probabilities of each path Signup and view all the answers

What is the key difference between independent and dependent events?

The effect of previous events on subsequent events Signup and view all the answers

What do the branches of a tree diagram represent?

Different outcomes of an event Signup and view all the answers

Why do we multiply the probabilities along a path in a tree diagram?

Because the probabilities need to be combined Signup and view all the answers

What is a key assumption when using tree diagrams to model dependent events?

The events are discrete Signup and view all the answers

A tree diagram is used to model the outcomes of two independent events, A and B. If P(A) = 0.4 and P(B) = 0.7, what is the probability that both events occur?

0.28 Signup and view all the answers

In a tree diagram, what is the purpose of the probability noted along each branch?

To determine the probability of the event Signup and view all the answers

A tree diagram is used to model the outcomes of three events, A, B, and C. If the probability of each event is 0.5, what is the probability that all three events occur?

0.125 Signup and view all the answers

What is the key difference between calculating the probability of a single path and the probability of multiple paths leading to a desired outcome?

The probability of multiple paths is always the sum of the individual probabilities Signup and view all the answers

A tree diagram is used to model the outcomes of two dependent events, A and B. If P(A) = 0.3 and P(B|A) = 0.6, what is the probability that both events occur?

0.18 Signup and view all the answers

What is a benefit of using tree diagrams to visualize the outcomes of a sequence of events?

They can be used to model dependent events Signup and view all the answers

A tree diagram is used to model the outcomes of two events, A and B. If the probability of each event is 0.4, what is the probability that at least one event occurs?

0.84 Signup and view all the answers

What is the primary condition for using the formula P(A and B) = P(A) × P(B) to calculate the probability of multiple events?

The events must be independent Signup and view all the answers

A tree diagram is used to model the outcomes of three events, A, B, and C. If the probability of each event is 0.6, what is the probability that exactly two events occur?

0.48 Signup and view all the answers

What is the purpose of multiplying the probabilities along a path in a tree diagram?

To find the probability of the sequence of events Signup and view all the answers

A tree diagram is used to model the outcomes of two events, A and B. If P(A) = 0.5 and P(B|A) = 0.8, what is the probability that event B occurs?

0.6 Signup and view all the answers

What is the primary advantage of using tree diagrams to model the outcomes of a sequence of events?

They provide a visual representation of the possible outcomes and their probabilities Signup and view all the answers

A tree diagram is used to model the outcomes of two independent events, A and B. If P(A) = 0.7 and P(B) = 0.3, what is the probability that at most one event occurs?

0.63 Signup and view all the answers

What is the primary assumption when using tree diagrams to model dependent events?

The probability of an event is unaffected by previous events Signup and view all the answers

A tree diagram is used to model the outcomes of three events, A, B, and C. If P(A) = 0.4, P(B) = 0.5, and P(C) = 0.6, what is the probability that at least one event occurs?