Independent and Dependent Probability

Front

What is independent probability?

Back

Independent probability refers to the likelihood of an event occurring that is not affected by the occurrence of another event. For example, flipping a coin and rolling a die are independent events.

Front

What is dependent probability?

Back

Dependent probability refers to the likelihood of an event occurring that is affected by the occurrence of another event. For example, drawing cards from a deck without replacement is a dependent event.

Front

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

Back

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

Front

How do you calculate the probability of dependent events occurring together?

Back

To find the probability of two dependent events A and B occurring together, multiply the probability of the first event by the conditional probability of the second event given the first: P(A and B) = P(A) * P(B|A).

Front

What is the probability of drawing two red cards from a deck without replacement?

Back

The probability of drawing two red cards from a standard deck of 52 cards is calculated as follows: P(Red 1) = 26/52, P(Red 2 | Red 1) = 25/51. Therefore, P(Red 1 and Red 2) = (26/52) * (25/51) = 25/102.

Front

If a bag contains 3 red and 2 blue marbles, what is the probability of drawing a red marble first and then a blue marble without replacement?

Back

P(Red first) = 3/5, P(Blue second | Red first) = 2/4. Therefore, P(Red and Blue) = (3/5) * (2/4) = 3/10.

Front

What is the total probability rule?

Back

The total probability rule states that if you have a set of mutually exclusive events, the total probability of an event can be found by summing the probabilities of the event occurring under each condition.

Front

What is the difference between theoretical and experimental probability?

Back

Theoretical probability is based on the expected outcomes of an event, while experimental probability is based on the actual results of an experiment.

Front

What is a 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

How do you determine if two events are independent?

Back

Two events A and B are independent if P(A and B) = P(A) * P(B). If this equality holds, the events do not influence each other.