Independent and Dependent Probability

Front

What is the definition of independent events in probability?

Back

Independent events are two or more events where the occurrence of one event does not affect the occurrence of the other.

Front

What is the definition of dependent events in probability?

Back

Dependent events are two or more events where the occurrence of one event affects the occurrence of the other.

Front

How do you determine if two events A and B are independent?

Back

If P(A) * P(B) = P(A ∩ B), then events A and B are independent.

Front

What is the formula for calculating the probability of independent events?

Back

P(A and B) = P(A) * P(B) for independent events.

Front

What is the formula for calculating the probability of dependent events?

Back

P(A and B) = P(A) * P(B|A) for dependent events.

Front

If a card is drawn from a deck and not replaced, what type of event is this?

Back

This is a dependent event because the outcome of the first draw affects the second draw.

Front

What is the probability of drawing two red cards from a stack of 5 red and 8 blue cards without replacement?

Back

5/39.

Front

If the probability of event A is 0.5 and event B is 0.3, what is the probability of both events occurring if they are independent?

Back

P(A and B) = 0.5 * 0.3 = 0.15.

Front

What is the probability of drawing a blue card first and then a red card from a stack of 5 red and 8 blue cards without replacement?

Back

P(Blue first) = 8/13; P(Red second) = 5/12; P(Blue and Red) = (8/13) * (5/12) = 40/156.

Front

What does it mean if two events are mutually exclusive?

Back

Mutually exclusive events cannot occur at the same time; the occurrence of one event means the other cannot occur.