Do the experiment results match the math?

Answer Key - Grade 7 Math Worksheet - Challenge Me

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

1. 1.

   Zee's spinner has 10 equal sections, some of them gold. The model predicts about 36 gold landings in 120 spins. How many sections are gold?

   3
2. 2.

   Esme's spinner has 8 equal sections, some of them gold. The model predicts about 150 gold landings in 200 spins. How many sections are gold?

   6
3. 3.

   Ren draws a tile from a bag of 20 tiles, some of them gold, and puts it back. The model predicts about 105 gold draws in 300 draws. How many tiles are gold?

   7
4. 4.

   Ren flips a coin 10 times and gets 7 heads. Zee flips another coin 400 times and gets 280 heads. Both shares are 70%. Whose result gives stronger reason to doubt a fair coin?

   • Zee's, because 280 is 80 over the expected 200, while 7 of 10 can easily happen by chance.
   • Neither, because a fair coin can give 70% heads in any run of flips, whether long or short.
   • Ren's, because with fewer flips each flip counts more toward the share of heads, so it is stronger.
   • They are equally strong, because both shares are 70% and a fair coin should give about 50%.
5. 5.

   Pia rolls a number cube 600 times and gets 112 sixes, where 100 are expected. Pia says the cube is rigged because 112 is not 100. What is the best response?

   • Sixes already came up extra times, so the next 600 rolls will give fewer than 100 sixes to balance it.
   • A fair cube gives exactly 100 sixes in 600 rolls, so a tally of 112 shows the cube is rigged.
   • The tally of 112 is under 1/5 of the rolls, and 1/5 is bigger than 1/6, so sixes are too rare.
   • The tally is 12 over in 600 rolls, about 18.7% against 16.7%, so the fair model seems reasonable.
6. 6.

   Tala drops a cup 30 times and it lands upright 9 times, so Tala predicts 90 uprights in 300 drops. Milo drops it 300 times and gets 71 uprights. What is the best conclusion?

   • The cup changed between the two runs, so neither share says anything about how the cup lands.
   • Milo must have made mistakes, since the model came from real drops, so 90 stays the right prediction.
   • Average the two shares, 30% and about 24%, to get 27%, since both runs count equally in the model.
   • The first 30 drops were a small sample, so the 300 drops are better evidence: about 24%, not 30%.
7. 7.

   A fair coin lands on heads 6 times in a row. Bo says tails is due on the next flip. What is the chance of tails on the next flip?

   • Less than 1/2, because heads is on a streak and a streak is likely to continue next.
   • 1/64, because six heads in a row shows how unlikely tails is.
   • 1/2, because each flip is separate and the earlier flips do not change the next one.
   • More than 1/2, because tails must catch up with heads over a long run of flips like this.
8. 8.

   Noah wants a model for how a thumbtack lands, point up or point down. The two ways may not be equally likely. Which plan gives the best model?

   • Toss it 5 times and use the share from those 5 tosses as the model for later tosses.
   • Say the model is 1/2 for each, because the tack can land in two ways, up or down.
   • Toss it 200 times but use just the first 20 tosses for the model, to save time.
   • Toss it 200 times, tally each way it lands, and use each share as the model.
9. 9.

   Ari wants to find out which of two spinners, A or B, lands on gold more often. Which plan is fairest?

   • Spin each one 200 times in the same way, then compare the gold shares.
   • Spin A hard 200 times and B gently 200 times, then compare the share of gold.
   • Spin each one 5 times in the same way and pick the one that lands on gold more.
   • Spin A 200 times and B 50 times, then compare the number of gold landings for each.
10. 10.

    Kira records the share of heads from a coin after 10, 100 and 1,000 flips: 70%, 56% and 51%. Which conclusion is best supported?

    • The share was above 50% each time, so the coin seems unfair and the model is wrong.
    • The share fell each time, so it will keep falling below 50% with more flips.
    • The share moves toward 50% as the flips grow, which supports a fair coin.
    • The 70% share after 10 flips is the real chance, and later shares are mistakes.