Independent and 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 two cards from a deck without replacement is a dependent event.

Front

What is the probability of drawing a king from a standard deck of cards?

Back

The probability of drawing a king from a standard deck of 52 cards is 4/52 or 1/13.

Front

If a card is drawn from a deck and replaced, what type of event is this?

Back

This is an independent event because replacing the card means the outcome of the first draw does not affect the second draw.

Front

What is the probability of drawing two hearts in a row from a deck of cards without replacement?

Back

The probability is (13/52) * (12/51) = 1/17.

Front

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

Back

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

Front

What is the probability of drawing a red marble from a bag containing 6 red and 4 blue marbles?

Back

The probability is 6/10 or 3/5.

Front

If you draw a red marble and do not replace it, what happens to the probability of drawing a blue marble next?

Back

The probability of drawing a blue marble increases because there is one less marble in total.

Front

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

Back

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

Front

What is the probability of picking a white rose first and a red rose next from a tray of 5 red, 3 yellow, and 8 white roses without replacement?

Back

The probability is (8/16) * (5/15) = 1/6.