Tree Diagrams - Midterm Exam Review

Front

What is a tree diagram?

Back

A tree diagram is a graphical representation used to illustrate all possible outcomes of a probability experiment, showing the paths leading to each outcome.

Front

How do you calculate the probability of two independent events occurring?

Back

To find the probability of two independent events A and B occurring, multiply their individual probabilities: P(A and B) = P(A) * P(B).

Front

What is conditional probability?

Back

Conditional probability is the probability of an event occurring given that another event has already occurred, denoted as P(A|B).

Front

What is the formula for conditional probability?

Back

The formula for conditional probability is P(A|B) = P(A and B) / P(B), where P(A and B) is the probability of both events occurring.

Front

If the probability of passing statistics is 0.3, what is the probability of failing statistics?

Back

The probability of failing statistics is 1 - P(pass) = 1 - 0.3 = 0.7.

Front

What is the total probability of passing any topic if the probability of passing is 0.8 for non-statistics topics?

Back

The total probability of passing any topic is a weighted average based on the probabilities of each topic.

Front

How do you find the probability of the union of two events?

Back

To find the probability of the union of two events A and B, use the formula: P(A or B) = P(A) + P(B) - P(A and B).

Front

What is the probability of selecting a blue brick after selecting a red brick from a box with 4 blue and 7 red bricks?

Back

If the first brick is red, the probability of selecting a blue brick second is 4/10 or 2/5.

Front

What is Bayes' theorem?

Back

Bayes' theorem relates the conditional and marginal probabilities of random events, allowing for the updating of probabilities based on new evidence.

Front

If the probability of a topic being statistics is 0.35, what is the probability of it being a non-statistics topic?

Back

The probability of a non-statistics topic is 1 - P(statistics) = 1 - 0.35 = 0.65.