Independent & Dependent Events

Front

What are 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. For example, flipping a coin and rolling a die are independent events.

Front

What are dependent events in probability?

Back

Dependent events are two or more events where the occurrence of one event affects the occurrence of the other. For example, drawing two cards from a deck without replacement is a dependent event.

Front

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

Back

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

Front

If you draw a card from a deck and do not replace it, what type of event is this?

Back

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

Front

What is the probability of drawing two aces in a row without replacement?

Back

The probability is 4/52 * 3/51 = 1/221.

Front

In a basket with 8 apples and 7 peaches, if you select a fruit, replace it, and select again, what type of events are these?

Back

These are independent events because replacing the fruit means the total number of fruits remains the same.

Front

What is the probability of drawing an even number from a set of cards numbered 1-10?

Back

There are 5 even numbers (2, 4, 6, 8, 10) out of 10, so the probability is 5/10 or 1/2.

Front

If you draw a red pen from a box of pens and do not replace it, what type of event is this?

Back

This is a dependent event because the total number of pens changes after the first draw.

Front

What is the probability of drawing a red marble and then a gray marble if the first marble is replaced?

Back

The probability is (3/18) * (4/18) = 1/27.

Front

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

Back

The probability of independent events A and B occurring is P(A) * P(B).