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.

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.

Front

How do you calculate the probability of independent events?

Back

To calculate the probability of independent events, multiply the probabilities of each event: P(A and B) = P(A) * P(B).

Front

How do you calculate the probability of dependent events?

Back

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

Front

Example of independent events: Flipping a coin and rolling a die. What is the probability of getting heads and a 4?

Back

P(Heads) = 1/2, P(4) = 1/6; P(Heads and 4) = (1/2) * (1/6) = 1/12.

Front

Example of dependent events: Drawing cards from a deck without replacement. What is the probability of drawing two aces?

Back

P(1st Ace) = 4/52, P(2nd Ace|1st Ace) = 3/51; P(Ace and Ace) = (4/52) * (3/51) = 1/221.

Front

What is the probability of selecting two male students from a class of 8 males and 7 females without replacement?

Back

P(1st Male) = 8/15, P(2nd Male|1st Male) = 7/14; P(Male and Male) = (8/15) * (7/14) = 28/105 = 26.7%.

Front

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

Back

P(1st Red) = 5/13, P(2nd Red|1st Red) = 4/12; P(Red and Red) = (5/13) * (4/12) = 20/156 = 5/39.

Front

What does it mean if two events are independent?

Back

If two events are independent, the occurrence of one event does not change the probability of the other event occurring.

Front

What does it mean if two events are dependent?

Back

If two events are dependent, the occurrence of one event affects the probability of the other event occurring.