Do the experiment results match the math?

Answer Key - Grade 7 Math Worksheet - Building Confidence

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

1. 1.

   Kira rolls a fair number cube 120 times and gets a 5 or 6 on 47 rolls. The model gives that a 1/3 chance. How far is 47 from the expected count?

   7
2. 2.

   Pia draws a card from a box of 12 cards, 5 of them red, and puts it back. After 144 draws, 51 were red. How far is 51 from the expected count?

   9
3. 3.

   A spinner has 10 equal sections, 4 of them with stars. Luz spins 250 times and lands on a star 112 times. How far is 112 from the expected number of stars?

   12
4. 4.

   Tala's fair coin should show about 50 heads in 100 flips. It showed 56 heads. Which statement fits best?

   • Because the tally is not exactly 50, the model seems wrong and the coin seems to be unfair.
   • The coin has a 56% chance of heads, because the tally shows 56 heads out of the 100 flips.
   • Heads got ahead, so the next 100 flips will show fewer than 50 heads to even out the total.
   • A gap of 6 in 100 flips is small enough for chance, so the model still seems reasonable.
5. 5.

   Bo's spinner has 4 equal sections, so red should come up about 100 times in 400 spins. Red came up 163 times. Which statement fits best?

   • Red got far ahead, so the next 400 spins will land on red fewer than 100 times to make up for it.
   • Tallies wobble around the expected count, so 163 is just chance and the equal-sections model seems fine.
   • The tally is 63 over the expected count, too big a gap for chance, so the model seems doubtful.
   • The tally of 163 is under half of the 400 spins, so the model seems reasonable.
6. 6.

   Esme flips a fair coin 10 times and gets 8 heads, where 5 are expected. Which statement fits best?

   • Heads are ahead, so tails will come up more in the next flips until the two totals even out.
   • Eight is 3 more than the expected 5, which is a big gap next to that count, so the coin seems unfair.
   • Heads came up 8 times in 10 flips, so the chance of heads should now be changed to 8/10.
   • Ten flips is a small sample and a gap of 3 can happen by chance, so the model seems reasonable.
7. 7.

   Jun flips a fair coin 50 times and gets 24 heads, where 25 are expected. Which statement fits best?

   • Since 24 is under half of 50, tails must have the higher chance of the two.
   • The result matches the model if the next 50 flips also show exactly 24 heads.
   • The tally is 1 away from the expected count, so the result matches the model well.
   • The tally is not 25, so the result does not match the model and the coin seems unfair.
8. 8.

   Milo rolls a fair number cube 12 times and gets only one 4, where 2 are expected. Milo says the cube is broken. What is the best response?

   • A fair cube must show each face exactly 2 times in 12 rolls, so this cube must be broken.
   • The cube is fair, so the next 12 rolls will show three 4s to make up for the one that is missing.
   • One 4 in 12 rolls means the chance of a 4 is 1/12, so the model should be changed to match it.
   • Twelve rolls is a small sample and one 4 is close to the 2 expected, so chance can explain it.
9. 9.

   Zee flips a fair coin 20 times, then 200, then 2,000. What usually happens to the share of heads as the flips grow?

   • The share of heads settles near 1/2, though the count of heads can still miss by more.
   • The share of heads moves away from 1/2, because small gaps add up over more and more flips.
   • The share of heads stays the same as in the first 20 flips, so more flips change nothing.
   • The count of heads gets closer and closer to exactly half the flips, so it misses by less.
10. 10.

    Ren's spinner has 3 equal sections, so red should come up about 10 times in 30 spins. Red came up 12 times. What is the best next step to check the model?

    • Stop now, since 12 is not the expected 10, so the model must be wrong.
    • Change the model to 12/30 right away and use that share for the predictions made later.
    • Spin many more times and compare the share of red each time with 1/3.
    • Spin 30 more times and trust whichever set of 30 is closer to 1/3.