Conditional Probability: Venn, Tree Diagrams, Tables

Front

What is conditional probability?

Back

The probability of an event occurring given that another event has already occurred.

Front

What is the formula for conditional probability?

Back

P(A | B) = P(A and B) / P(B), where P(A | B) is the probability of A given B.

Front

What does P(A | B) represent?

Back

The probability of event A occurring given that event B has occurred.

Front

How do you calculate the probability of survival for a specific group, such as first-class passengers on the Titanic?

Back

By using the formula for conditional probability: P(Survival | First Class) = Number of survivors in first class / Total number of first-class passengers.

Front

What is a tree diagram used for in probability?

Back

A tree diagram visually represents the possible outcomes of a probability experiment and helps in calculating probabilities of compound events.

Front

In a tree diagram, what does the denominator represent when calculating conditional probabilities?

Back

The denominator represents the total probability of the condition that has already occurred.

Front

What is the meaning of P(B | A')?

Back

The probability of event B occurring given that event A has not occurred.

Front

How do you interpret the result of P(B | A') = 0.7?

Back

It means that there is a 70% chance that event B occurs given that event A did not occur.

Front

What does P(not sport | Foreign language) represent?

Back

The probability of not participating in sports given that a student is taking a foreign language.

Front

How do you find the probability of an event not occurring?

Back

P(not A) = 1 - P(A), where P(A) is the probability of event A occurring.