PROBABILITY: Independent & Dependent Events

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(s).

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(s).

Front

If you draw a card from a deck and replace it before drawing again, are the events independent or dependent?

Back

Independent.

Front

If you draw a card from a deck and do not replace it before drawing again, are the events independent or dependent?

Back

Dependent.

Front

What is the probability of drawing two apples from a basket containing 8 apples and 7 peaches with replacement?

Back

(8/15) * (8/15) = 64/225.

Front

What is the probability of drawing two apples from a basket containing 4 apples and 6 peaches without replacement?

Back

(4/10) * (3/9) = 12/90 = 2/15.

Front

In a sock drawer with 6 white, 4 brown, and 6 black socks, what is the probability of picking a white sock and then a brown sock without replacement?

Back

(6/16) * (4/15) = 24/240 = 1/10.

Front

In a sock drawer with 4 white, 6 brown, and 2 black socks, what is the probability of picking a white sock and then a brown sock without replacement?

Back

(4/12) * (6/11) = 24/132 = 2/11.

Front

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

Back

P(A and B) = P(A) * P(B).

Front

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

Back

P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B given A has occurred.