Independent or dependent? Does putting it back matter?

Answer Key - Grade 8 Math Worksheet

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

1. 1.

   Ari flips a fair coin and gets heads 4 times in a row. Is the next flip independent of the first four, or dependent on them?

   • Dependent: after 4 heads, tails is more likely, as the coin remembers
   • Dependent: the same coin is flipped each time
   • Independent: the coin is the same, so heads is still 1/2
2. 2.

   Bo spins a spinner with 4 equal parts (red, blue, yellow, green) twice. Are the two spins independent or dependent?

   • Dependent: the same spinner is used twice
   • Independent: the spinner is the same for both spins
   • Dependent: the arrow is less likely to stop on the same color twice
3. 3.

   Esme deals two cards, without looking, from a pile of 10 number cards. The first card is not put back. Are the two cards independent or dependent?

   • Independent: the pile was shuffled first
   • Dependent: the first card is not put back, so the pile changes
   • Independent: cards have numbers, not colors, so the pile cannot change
4. 4.

   Jun's teacher picks two class helpers by drawing names from a hat of 25, without looking. The first name stays out. Independent or dependent?

   • Independent: each name is drawn without looking
   • Dependent: the first name stays out, so the hat changes
   • Independent: there are many names
5. 5.

   Kira's bag holds 7 red and 5 blue marbles. Kira draws a blue marble without looking and keeps it out. What is the chance the next draw is blue, in simplest form?

   4/11
6. 6.

   Luz's bag holds 3 red, 4 blue and 5 green marbles. Luz draws a green marble without looking and keeps it out. What is the chance the next draw is red, in simplest form?

   3/11
7. 7.

   Milo has cards numbered 1 to 20 in a bag. Milo draws the card 8 without looking and keeps it out. What is the chance the next card is odd, in simplest form?

   10/19
8. 8.

   Noah's bag holds 5 red and 7 blue marbles. Noah draws a red marble without looking and puts it back. What is the chance the next draw is red, in simplest form?

   5/12
9. 9.

   Tala's bag has 3 red and 5 blue marbles. The first draw, without looking, is red. Is a red second draw more likely if the first is put back, or kept out?

   • The same: the bag started the same both ways
   • Put back: 3/8 is more than 2/7
   • Kept out: 2/7 is more than 3/8
10. 10.

    Ari's bag has 2 green and 4 white marbles. The first draw, without looking, is green. Is a green second draw more likely if the first is put back, or kept out?

    • Kept out: 1/5 is more than 1/3
    • Put back: 1/3 is more than 1/5
    • The same: the bag started the same both ways