Use random numbers to copy a chance situation

Answer Key - Grade 7 Math Worksheet - Challenge Me

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

1. Read this first

   Use this

   Digits 0 to 3 are star cards. Each trial stops at its first digit from 0 to 3. Trials: 5 7 2 | 1 | 6 9 4 8 0 | 9 3 | 4 5 6 7 8 3 | 0 | 8 4 2 | 7 6 1 | 3 | 9 8 8 9 5 1 | 6 2 | 4 7 9 0.

2. 1.

   Ari draws a card at random until a star shows, putting each back (40% are stars). From the trials shown, what is the estimated chance it takes at least 4 draws, in simplest form?

   1/3

3. Use this

   Digits 0 and 1 are a prize. Each trial stops at its first 0 or 1. Trials: 5 8 0 | 4 6 7 1 | 9 1 | 8 2 6 4 1 | 7 3 9 0 | 1 | 2 4 0 | 4 4 9 5 7 0 | 0 | 6 3 1 | 9 7 4 5 1 | 8 0.

4. 2.

   One box in 5 holds a prize. Bo opens boxes at random until a prize shows. From the trials shown, what is the estimated chance it takes at least 3 boxes, in simplest form?

   2/3

5. Use this

   Digits 0 to 2 are rain. Each trial stops at its first digit from 0 to 2. Trials: 5 8 7 1 | 3 0 | 9 2 | 4 7 9 8 5 0 | 8 1 | 7 7 2 | 6 4 9 1 | 2 | 9 5 8 3 8 0 | 5 4 0 | 1 | 8 9 6 7 4 2.

6. 3.

   Each day has a 30% chance of rain. Esme counts days until the first rain. From the trials shown, what is the estimated chance it takes at least 3 days, in simplest form?

   7/12

7. Use this

   Digits 0 to 4 are made shots. Each trial stops at its first digit from 0 to 4. Trials: 6 4 | 9 1 | 8 7 0 | 5 2 | 7 9 8 3 | 6 4 | 9 7 6 0 | 2 | 8 3 | 9 9 7 4 | 7 6 8 6 1 | 5 1.

8. 4.

   A player makes half of shots. Jun counts shots until the first made shot. From the trials shown, what is the estimated chance it takes at least 3 shots, in simplest form?

   5/12
9. 5.

   Luz draws 2 cards from a hat of 5 (2 red) without putting the first back. Digits 0 to 4 are the cards, 0 and 1 red; two digits per trial. What needs fixing?

   • The hat has 5 cards, so each trial needs 5 digits instead of 2, one digit for each card in the hat.
   • A digit can repeat, but a card cannot be drawn twice, so skip any trial with a repeated digit.
   • Nothing needs fixing, because drawing without putting back works the same as drawing with putting back.
   • Digits 0 and 1 are too few for red, so 0 to 3 should be red to match the 2 red cards in the hat.
10. 6.

    Milo simulates two flips of a fair coin for 8 trials, and 3 show two heads. Milo says the chance is 3/8, so the coin is rigged. What is the best response?

    • The coin is rigged, because 3/8 is more than the 1/4 chance of two heads, so the model must be wrong.
    • Run 8 more trials and average the two results together to get exactly 1/4 for the chance of two heads.
    • Eight trials is too few to settle anything; run many more trials and see where the share goes.
    • 3/8 is right, because the trials are real outcomes, and real outcomes cannot be wrong or misleading.
11. 7.

    Pia simulated 60 turns of two free throws, and both shots were made in 18 of them. About how many of 500 real turns should end with both shots made?

    150
12. 8.

    Ren simulated 40 weekends, and it rained on both days in 12 of them. About how many of 300 weekends like these should have rain on both days?

    90
13. 9.

    Tala simulated 50 pairs of spins, and the two spins matched in 21 pairs. About how many of 200 pairs of spins should match?

    84
14. 10.

    Zee simulated 30 pairs of marble draws, and 9 pairs had two red marbles. About how many of 250 pairs of draws should have two red marbles?

    75