Worksheet

Game Studio: Balance the Challenge

Interpret probabilities from 0 to 1 while checking video game levels, score rules, and balancing decisions.

Grade 7MathInteractive · Printable

Aligned to7.SP.C.5

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Single worksheet
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1 Common Core standard
Printable answer key
14 questions
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Details

Format: Interactive · Printable
Grade: Grade 7
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

Students interpret probabilities from 0 to 1 as measures of an event's likelihood.
Students distinguish impossible, unlikely, equally likely, likely, and certain events.
Students use probability values to evaluate level-balancing decisions.

How to use

Use after introducing the probability scale. Have students work independently, then discuss how score amounts differ from the chances of earning them.

Curriculum

Common Core standard covered

7.SP.C.5

Understand probability as a number from 0 to 1 showing how likely an event is, from impossible to certain.

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Game Studio: Balance the Challenge

Use probabilities to interpret level difficulty and score events.

Check the Score Rules

Use each stated game rule. A probability describes a chance, not a number of points.

In one level, the final score must be a whole number from 0 through 80. The studio checks the event “a player earns 90 points.”

What is the probability of this event?

Every completed tutorial awards exactly 12 points. A tester completes the tutorial. Which statement correctly describes the chance of earning 12 points?

A. The probability is 12 because the award is 12 points.
B. The probability is 1 because the award is guaranteed.
C. The probability is 0 because the score cannot change.
D. The probability is 0.5 because there is one possible award.

A bonus has a probability of 0.08 of appearing. When it appears, it awards 500 points. Which note correctly separates chance from score?

A. The bonus is impossible to receive because its chance is small.
B. The bonus is unlikely to appear even though its award is large.
C. The bonus is certain to appear because its award is positive.
D. The bonus is likely to appear because it awards many points.

A settings panel requires a probability between 0 and 1, including both endpoints. Select every entry that the panel should reject.

−0.1501.057/81

The chance of unlocking a hidden room is greater than 0 but less than 0.1. Which description must be true?

A. Unlocking the room is possible but unlikely.
B. Unlocking the room is certain.
C. Unlocking the room is impossible.
D. Unlocking the room is more likely than not.

Make Balance Decisions

Treat the listed probabilities as the studio's models for one attempt. Compare likelihoods, not point values.

The studio wants a practice level where earning a medal and not earning a medal are equally likely. Which proposed probability of earning a medal meets that goal?

A. The proposed probability is 1.
B. The proposed probability is 1/4.
C. The proposed probability is 3/4.
D. The proposed probability is 1/2.

The studio wants clearing the opening level to be very likely, but not certain. Which proposed setting best fits?

Opening-Level Settings
Setting	Probability of clearing
Gentle	0.96
Balanced	0.5
Demanding	0.18
Automatic	1

A. Use the Balanced setting.
B. Use the Automatic setting.
C. Use the Demanding setting.
D. Use the Gentle setting.

Two versions of a jump have clearance probabilities of 0.39 and 0.61. The studio chooses the version where clearing the jump is less likely than missing it.

Write the probability of clearing the chosen version.

A patch changes the probability of earning a speed badge from 0.77 to 0.58. Which statement correctly describes the patched level?

A. Earning the badge is still likely, but less likely than before.
B. Earning the badge is now more likely than before the patch.
C. Earning the badge is now equally likely as not earning it.
D. Earning the badge is now unlikely because its probability decreased.

10.

The studio compares three score events for one level.

Score Event Models
Event	Probability
Score below 100	0.25
Score exactly 100	0.15
Score above 100	0.6

Select every supported statement.

Scoring exactly 100 is impossible.Scoring above 100 is more likely than scoring below 100.Scoring below 100 is more likely than scoring exactly 100.Scoring above 100 is certain.Scoring exactly 100 is less likely than not scoring exactly 100.

Review the Design Notes

Check the meaning of each probability. Explain your reasoning in the final item.

11.

A designer writes, “A perfect score should be closer to impossible than to an even chance, but it must remain possible.” Which proposed probability satisfies this note?

A. Set the probability to 0.30.
B. Set the probability to 0.00.
C. Set the probability to 0.12.
D. Set the probability to 0.50.

12.

An optional shield has a probability of 0.99 of blocking a hit. The studio replaces it with a shield that is certain to block a hit.

What probability describes the replacement shield blocking a hit?

13.

A review note lists the probability of earning a gold rank as 0.49. A designer rounds it to 0.5 and labels it “equally likely.” Which revision preserves the meaning of the original value?

A. Keep 0.49 and say earning gold is slightly more likely than not.
B. Keep 0.49 and say earning gold is impossible rather than unlikely.
C. Keep 0.49 and say earning gold is slightly less likely than not.
D. Keep 0.49 and say earning gold and not earning gold are equally likely.

14.

A level can end with a score of 0, 50, or 100 points. The probability of scoring 100 is 0.5. Noor says, “That means all three scores are equally likely.” Explain why Noor's conclusion does not follow. State what the probability of 0.5 actually tells us.