You roll a standard six-sided die and then flip a fair coin. Which statement best describes these two events?

The events are dependent because they happen in sequence.

The events are independent because the outcome of the die roll does not affect the outcome of the coin flip.

The events are dependent because the total number of outcomes is 12.

The events are independent because they both involve chance.

In an experiment where you draw two cards from a deck without replacement, why are the events considered dependent?

Because the total number of cards and the number of specific cards both decrease after the first draw.

Because the color of the first card drawn is unknown.

Because the second card drawn is always different from the first.

Because card drawing is always a dependent event.

Finding the Probability of Independent and Dependent Events Practice — Grade 9 math

Lesson 33: Finding the Probability of Independent and Dependent Events — Practice Questions

1. You roll a standard six-sided die and then flip a fair coin. Which statement best describes these two events?
- A. The events are dependent because they happen in sequence.
- B. The events are independent because the outcome of the die roll does not affect the outcome of the coin flip.
- C. The events are dependent because the total number of outcomes is 12.
- D. The events are independent because they both involve chance.
2. A drawer contains 5 black socks and 7 white socks. You randomly pick one sock, do not replace it, and then pick a second. What is the probability both socks are black? Express your answer as a simplified fraction. ___
3. A bag contains 3 green balls and 5 yellow balls. You draw a ball, replace it, and then draw a second ball. What is the probability that you draw a green ball both times? Express your answer as a fraction. ___
4. A bag has 4 red and 6 blue marbles. You draw one marble, do not replace it, then draw a second. What is the probability the first is red and the second is blue? Express your answer as a simplified fraction. ___
5. In an experiment where you draw two cards from a deck without replacement, why are the events considered dependent?
- A. Because the total number of cards and the number of specific cards both decrease after the first draw.
- B. Because the color of the first card drawn is unknown.
- C. Because the second card drawn is always different from the first.
- D. Because card drawing is always a dependent event.
6. A bag contains 8 red and 4 green marbles. Two marbles are drawn without replacement. What is the probability that both marbles drawn are red? Express as a simplified fraction: ___.
7. A class has 12 boys and 10 girls. If two students are randomly selected without replacement, what is the probability that the first is a girl and the second is a boy?
- A. $\frac{60}{242}$
- B. $\frac{20}{77}$
- C. $\frac{132}{484}$
- D. $\frac{10}{21}$
8. From a standard 52-card deck, two cards are drawn without replacement. What is the probability of drawing a King and then a Queen? Express your answer as a simplified fraction: ___.
9. A drawer contains 10 blue socks and 6 black socks. If two socks are drawn randomly without replacement, what is the probability that both socks are black?
- A. $\frac{1}{8}$
- B. $\frac{9}{64}$
- C. $\frac{3}{20}$
- D. $\frac{1}{10}$
10. Which statement best describes why drawing two items from a bag without replacement are considered dependent events?
- A. The probability of the second event is always smaller than the first.
- B. The outcome of the first draw affects the probabilities for the second draw.
- C. The items are identical.
- D. The probability is found by adding the individual probabilities.