Independent or dependent? Does putting it back matter?

Grade 8 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

3 green, 2 yellow. Bo's bag holds 4 green and 2 yellow marbles. Bo draws a green marble without looking and keeps it out. What is the chance the next draw is green, in simplest form?
2 red, 3 white (the red one went back). Esme's bag holds 2 red and 3 white marbles. Esme draws a red marble without looking and puts it back. What is the chance the next draw is red, in simplest form?
1, 2, 4, 5, 6, 7, 8, 9, 10. Jun has cards numbered 1 to 10 in a bag. Jun draws the card 3 without looking and keeps it out. What is the chance the next card is even, in simplest form?
4.
Kira rolls a fair number cube, then rolls it again. Are the two rolls independent or dependent?
- Independent: the cube is the same for both rolls
- Dependent: the second roll comes later than the first
- Dependent: the same cube is used twice
5.
Luz draws a marble from a bag without looking, keeps it out, then draws again. Are the two draws independent or dependent?
- Independent: marbles cannot remember what was drawn before them
- Independent: both draws are done the same way, so nothing changes
- Dependent: the first marble is kept out, so the bag changes
6.
Milo draws a marble from a bag without looking, puts it back, then draws again. Are the two draws independent or dependent?
- Dependent: both draws come from the same bag, so they are linked
- Independent: the marble goes back, so the bag is the same
- Dependent: the second draw is harder
7.
Noah's class draws two names from a hat, without looking, for two jobs. The first name is not put back. Are the two draws independent or dependent?
- Independent: the jobs are different, so the names do not matter
- Dependent: the first name stays out, so the hat changes
- Independent: every name was in the hat at the start
Pia's bag holds 5 red and 3 blue marbles. Pia draws a red marble without looking and keeps it out. What is the chance the next draw is red, in simplest form?
Ren's bag holds cards numbered 1 to 6. Ren draws the card 2 without looking and puts it back. What is the chance the next draw is even, in simplest form?
Tala's bag holds 4 blue and 4 green marbles. Tala draws a blue marble without looking and keeps it out. What is the chance the next draw is green, in simplest form?

Independent or dependent? Does putting it back matter?

Answer Key - Grade 8 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

3 green, 2 yellow. Bo's bag holds 4 green and 2 yellow marbles. Bo draws a green marble without looking and keeps it out. What is the chance the next draw is green, in simplest form?
3/5
2 red, 3 white (the red one went back). Esme's bag holds 2 red and 3 white marbles. Esme draws a red marble without looking and puts it back. What is the chance the next draw is red, in simplest form?
2/5
1, 2, 4, 5, 6, 7, 8, 9, 10. Jun has cards numbered 1 to 10 in a bag. Jun draws the card 3 without looking and keeps it out. What is the chance the next card is even, in simplest form?
5/9
4.
Kira rolls a fair number cube, then rolls it again. Are the two rolls independent or dependent?
- Independent: the cube is the same for both rolls
- Dependent: the second roll comes later than the first
- Dependent: the same cube is used twice
5.
Luz draws a marble from a bag without looking, keeps it out, then draws again. Are the two draws independent or dependent?
- Independent: marbles cannot remember what was drawn before them
- Independent: both draws are done the same way, so nothing changes
- Dependent: the first marble is kept out, so the bag changes
6.
Milo draws a marble from a bag without looking, puts it back, then draws again. Are the two draws independent or dependent?
- Dependent: both draws come from the same bag, so they are linked
- Independent: the marble goes back, so the bag is the same
- Dependent: the second draw is harder
7.
Noah's class draws two names from a hat, without looking, for two jobs. The first name is not put back. Are the two draws independent or dependent?
- Independent: the jobs are different, so the names do not matter
- Dependent: the first name stays out, so the hat changes
- Independent: every name was in the hat at the start
Pia's bag holds 5 red and 3 blue marbles. Pia draws a red marble without looking and keeps it out. What is the chance the next draw is red, in simplest form?
4/7
Ren's bag holds cards numbered 1 to 6. Ren draws the card 2 without looking and puts it back. What is the chance the next draw is even, in simplest form?
1/2
Tala's bag holds 4 blue and 4 green marbles. Tala draws a blue marble without looking and keeps it out. What is the chance the next draw is green, in simplest form?
4/7