Probability Test 3 Fall 2024

Front

What is the probability of an event?

Back

The probability of an event is a measure of the likelihood that the event will occur, expressed as a number between 0 and 1.

Front

Define theoretical probability.

Back

Theoretical probability is the probability of an event calculated based on the possible outcomes in a perfect scenario, without any experimental data.

Front

What is the complement of an event?

Back

The complement of an event A, denoted as A', is the event that A does not occur. It is calculated as P(A') = 1 - P(A).

Front

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

Back

For independent events, the probability of both events A and B occurring is P(A and B) = P(A) * P(B).

Front

What is the formula for calculating the probability of an event happening at least once?

Back

To find the probability of an event happening at least once, use P(at least one) = 1 - P(none).

Front

If a die is rolled, what is the probability of rolling a number greater than 4?

Back

The probability of rolling a number greater than 4 (5 or 6) is P = 2/6 = 1/3.

Front

What is the probability of drawing a specific color marble from a bag?

Back

The probability of drawing a specific color marble is calculated as P(color) = (Number of that color marbles) / (Total number of marbles).

Front

Explain 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 law of large numbers?

Back

The law of large numbers states that as the number of trials increases, the experimental probability will converge to the theoretical probability.

Front

How do you find the expected value of a random variable?

Back

The expected value is calculated as E(X) = Σ [x * P(x)], where x is the value and P(x) is the probability of x.