Independent or dependent? Does putting it back matter?
Grade 8 Math Worksheet
Circle the best answer, or write your answer on the line.
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
Bo spins a spinner with 4 equal parts (red, blue, yellow, green) twice. Are the two spins independent or dependent?
- Independent: the spinner is the same for both spins
- Dependent: the same spinner is used twice
- Dependent: the arrow is less likely to stop on the same color twice
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?
- Dependent: the first card is not put back, so the pile changes
- Independent: the pile was shuffled first
- Independent: cards have numbers, not colors, so the pile cannot change
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: there are many names
- Independent: each name is drawn without looking
- Dependent: the first name stays out, so the hat changes
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?
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?
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
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
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?
Ren's bag holds 3 yellow and 7 green marbles. Ren draws a green marble without looking and keeps it out. What is the chance the next draw is green, in simplest form?