Probability of Independent and Dependent Events

Front

What is the definition of independent events in probability?

Back

Independent events are events where the outcome of one event does not affect the outcome of another event.

Front

What is the definition of dependent events in probability?

Back

Dependent events are events where the outcome of one event affects the outcome of another event.

Front

If a marble is drawn from a container and replaced before drawing a second marble, are the events independent or dependent?

Back

The events are independent.

Front

What is the probability of rolling a number greater than 4 on a standard number cube?

Back

The probability is 1/3, as there are 2 favorable outcomes (5 and 6) out of 6 possible outcomes.

Front

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

Back

The probability is 1/5, as there are 5 even numbers (2, 4, 6, 8, 10) out of 10 possible outcomes.

Front

When spinning a spinner twice, what is the probability of landing on red first and then blue if the events are independent?

Back

The probability is the product of the individual probabilities of landing on red and blue.

Front

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

Back

P(A and B) = P(A) * P(B) for independent events A and B.

Front

What is the probability of drawing a card with an even number and then a card greater than or equal to five if the first card is replaced?

Back

The probability is 3/10, as there are 3 even numbers (2, 4, 6, 8, 10) and 5 numbers greater than or equal to 5.

Front

What is the probability of selecting a gumball first and then a lollipop from a treat bag without replacement?

Back

The probability is 4/15, calculated as (4/10) * (6/9) for gumball then lollipop.

Front

What is the difference between replacement and no replacement in probability?

Back

Replacement means the first item is returned before the second selection, while no replacement means the first item is not returned.