Probability of Independent and Dependent Events

Front

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

Back

There are 3 odd numbers (1, 3, 5) on a number cube. Therefore, the probability is 3/6 or 1/2.

Front

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

Back

The probability of rolling an odd number on the first roll is 1/2, and the same for the second roll. Therefore, the probability of both events is (1/2) * (1/2) = 1/4.

Front

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

Back

There are 4 aces in a deck of 52 cards. Therefore, the probability is 4/52 or 1/13.

Front

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

Back

The probability of drawing the first ace is 4/52. After drawing one ace, there are 3 aces left and 51 cards total. So, the probability of drawing a second ace is 3/51. Therefore, the combined probability is (4/52) * (3/51) = 1/221.

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, rolling a die and flipping a coin.

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.

Front

If a red marble is drawn from a bag and not replaced, what is the nature of the next draw?

Back

The events are dependent because the first draw affects the total number of marbles and the composition of the bag.

Front

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

Back

There are 3 even numbers (2, 4, 6) on a number cube. Therefore, the probability is 3/6 or 1/2.

Front

What is the probability of rolling an even number first and an odd number second on a number cube?

Back

The probability of rolling an even number first is 1/2, and the same for rolling an odd number second. Therefore, the combined probability is (1/2) * (1/2) = 1/4.

Front

What is the probability of landing on red and then blue when spinning a spinner?

Back

If the spinner has equal sections, the events are independent. The probability of landing on red first and blue second is the product of their individual probabilities.