Independent or dependent? Does putting it back matter?
Grade 8 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
Jun's bag has 5 red and 3 blue marbles. The first draw, without looking, is red. How much more likely is blue next if it is kept out than if put back?
Kira's bag holds 4 red and 5 blue marbles. Kira draws two red marbles without looking and keeps them out. What is the chance the next draw is red, in simplest form?
Luz has cards numbered 1 to 10 in a bag. Luz draws the cards 3 and 8 without looking and keeps them out. What is the chance the next card is even, in simplest form?
Noah draws a card without looking, puts it back, shuffles, and draws again. Are the two draws independent or dependent?
- Independent: the card goes back, so the pile is the same
- Dependent: the same card is less likely to come up twice
- Dependent: both cards come from one pile
Pia's coach picks 2 of 6 runners, without looking, by drawing name cards. Cards are not put back. Are the two picks independent or dependent?
- Dependent: the first runner cannot be picked again, so 5 are left
- Independent: every runner had the same chance at the start
- Independent: the coach likes everyone
Ren's spinner has 2 equal parts, red and blue. It has landed on red 5 times in a row. Is the next spin independent of those, or dependent on them?
- Dependent: the same spinner is spun every time
- Independent: the spinner is the same, so red is still 1/2
- Dependent: blue is due after 5 reds
Tala's bag has 2 red, 3 blue and 5 green marbles. The first draw, without looking, is red. Is a green second draw more likely if the first is put back, or kept out?
- Kept out: 5/9 is more than 1/2
- The same: no green marble was touched
- Put back: 1/2 is more than 5/9
Zee's bag has 2 red, 3 blue and 5 green marbles. The first draw, without looking, is red. Is a red second draw more likely if the first is put back, or kept out?
- Kept out: 1/9 is more than 1/5
- The same: the bag started the same both ways
- Put back: 1/5 is more than 1/9
Ari draws the card 12, without looking, from cards numbered 1 to 12. Is drawing the 12 again more likely if the card is put back, or kept out?
- The same: each card had a chance of 1/12
- Kept out: the chance grows to 1/11
- Put back: 1/12 is more than 0
Zee's bag holds 4 red and 4 blue marbles. Zee draws one without looking, keeps it out, then draws again. Are the two draws independent or dependent?
- Independent: the bag had equal colors at the start
- Dependent: the first marble is kept out, so the bag changes
- Independent: each marble is drawn without looking, so the bag is fair
