Worksheet

Independent or dependent? Does putting it back matter?

Grade 8 Math Worksheet

NameDate

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

  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?

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

  2. 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

  3. 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
    • Independent: there are many names
    • Dependent: the first name stays out, so the hat changes

  4. 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?

  5. 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?

  6. 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?

  7. 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?

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

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

    • Kept out: 5/7 is more than 5/8
    • The same: the blue marbles were not touched
    • Put back: 5/8 is more than 5/7

  9. 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?

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

  10. Pia's bag holds 4 red and 6 blue marbles. Pia draws a red marble without looking and puts it back. What is the chance the next draw is blue, in simplest form?

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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. 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?

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

  2. 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

  3. 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
    • Independent: there are many names
    • Dependent: the first name stays out, so the hat changes

  4. 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

  5. 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

  6. 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

  7. 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?

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

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

    • Kept out: 5/7 is more than 5/8
    • The same: the blue marbles were not touched
    • Put back: 5/8 is more than 5/7

  9. 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?

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

  10. Pia's bag holds 4 red and 6 blue marbles. Pia draws a red marble without looking and puts it back. What is the chance the next draw is blue, in simplest form?

    3/5