Independent vs. Dependent Events

Front

What are independent events in probability?

Back

Independent events are events where the outcome of one event does not affect the outcome of another. For example, flipping a coin and rolling a die are independent events.

Front

What are dependent events in probability?

Back

Dependent events are events where the outcome of one event affects the outcome of another. For example, drawing a card from a deck and not replacing it before drawing another card.

Front

If a red marble is drawn from a bag and not replaced, what type of event is drawing a second marble?

Back

Dependent event, because the first draw affects the second.

Front

What is the probability of drawing a red marble from a bag containing 3 red, 4 gray, 6 white, and 5 black marbles?

Back

The probability is 3/18 or 1/6.

Front

If a marble is drawn and replaced, what type of events are drawing the first and second marbles?

Back

Independent events, because the replacement means the first draw does not affect the second.

Front

What is the probability of rolling an even number on a die?

Back

The probability is 3/6 or 1/2, since there are three even numbers (2, 4, 6) on a die.

Front

What is the probability of rolling an odd number on a die?

Back

The probability is 3/6 or 1/2, since there are three odd numbers (1, 3, 5) on a die.

Front

If the first roll of a die is a 4, what is the probability of rolling a 3 on the second roll?

Back

1/6, because the rolls are independent.

Front

What is the combined probability of rolling an even number first and an odd number second?

Back

1/2 (even) * 1/2 (odd) = 1/4.

Front

In a bag with 10 marbles, if 4 are red and 6 are blue, what is the probability of drawing a red marble and then a blue marble without replacement?

Back

The probability is (4/10) * (6/9) = 24/90 or 4/15.