Independent or dependent? Does putting it back matter?

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. 1.

   Esme's bag has 4 red and 2 blue marbles. The first draw, without looking, is red. How much more likely is red next if it is put back than if kept out?

   1/15
2. 2.

   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?

   3/56
3. 3.

   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?

   2/7
4. 4.

   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?

   1/2
5. 5.

   Milo's bag holds 6 green and 6 yellow marbles. Milo draws two green marbles without looking and keeps them out. What is the chance the next draw is green, in simplest form?

   2/5
6. 6.

   Noah draws a card without looking, puts it back, shuffles, and draws again. Are the two draws independent or dependent?

   • Dependent: both cards come from one pile
   • Independent: the card goes back, so the pile is the same
   • Dependent: the same card is less likely to come up twice
7. 7.

   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?

   • Independent: the spinner is the same, so red is still 1/2
   • Dependent: the same spinner is spun every time
   • Dependent: blue is due after 5 reds
8. 8.

   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
9. 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
   • Put back: 1/12 is more than 0
   • Kept out: the chance grows to 1/11
10. 10.

    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: each marble is drawn without looking, so the bag is fair
    • Independent: the bag had equal colors at the start
    • Dependent: the first marble is kept out, so the bag changes