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.

   Ari spins a spinner with 8 equal sections, 3 of them blue, 200 times and lands on blue 88 times. How far is 88 from the number of blue landings the model predicts?

   13
2. 2.

   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
3. 3.

   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
4. 4.

   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
5. 5.

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

   • 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.
   • Because the tally is not exactly 50, the model seems wrong and the coin seems to be unfair.
6. 6.

   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.
   • The tally is 63 over the expected count, too big a gap for chance, so the model seems doubtful.
   • Tallies wobble around the expected count, so 163 is just chance and the equal-sections model seems fine.
   • The tally of 163 is under half of the 400 spins, so the model seems reasonable.
7. 7.

   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?

   • Twelve rolls is a small sample and one 4 is close to the 2 expected, so chance can explain it.
   • One 4 in 12 rolls means the chance of a 4 is 1/12, so the model should be changed to match it.
   • 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.
8. 8.

   Noah and Bo each spin the same fair spinner 40 times. Noah gets 13 blue and Bo gets 9 blue. Why can the tallies differ when the spinner and the model are the same?

   • The first person to spin has a better chance of landing on blue, so that person gets more.
   • The model changes each time the spinner is used, so the expected count has to change too.
   • A fair spinner gives the same tally each time, so one of the two spinners must be unfair.
   • Each spin is random, so tallies from the same spinner vary from one set of spins to the next.
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 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 share of heads settles near 1/2, though the count of heads can still miss by more.
   • 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.