Two independent locks each turn blue or gold.

The sample space has four equally likely outcomes: BB, BG, GB, GG. Only GG opens the vault.

1 favorable outcome ÷ 4 total outcomes = 1/4 = 25%.

Grade 7 Math • 7.SP.8a

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Four dam gates are equally likely to open. Only one is gold.

Probability = favorable outcomes ÷ total outcomes

1/4 = 25%

That calculation works because every gate has an equal chance of being selected—a uniform probability model.

Grade 7 Math • 7.SP.7a

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Nine of ten test cars cleared the jump, so the experimental probability of success is 9/10, or 90%.

That predicts long-run frequency—not the guaranteed result of the next trial. More repeated trials generally produce a stronger estimate.

Grade 7 Math • 7.SP.6

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An 80% chance of success means the rescue is likely—not guaranteed.

Since 80% = 0.8 and 0.8 is close to 1, success is likely. But only a probability of 1 means certain.

Probability describes long-run likelihood, not the guaranteed outcome of one trial.

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Can one team be taller on average if individual heights overlap?

Yes. Averages describe overall patterns, not every person. Measures of center show what is typical, while variability shows the spread within each sample.
That distinction drives Grade 7 Math standard 7.SP.4.

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Can water samples describe an entire bay?

Repeated random samples might estimate pollutant levels of 4, 5, and 4 parts per million.

The results vary slightly, but their similarity supports an estimate of about 4–5 parts per million.

California standard 7.SP.2.

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A factory cannot test every power cell, so it selects a sample.

Random selection gives every cell a chance to be tested, making the sample more likely to represent the full production run.

How a sample is selected matters.

California Grade 7 standard 7.SP.1.

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A cargo bay measures 4 meters long, 3 meters wide, and 2 meters high.

V = 4 × 3 × 2 = 24 cubic meters.

Volume measures three-dimensional space, so the answer uses cubic units.

California Grade 7 standard 7.G.6.

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Two starship flight paths cross. One angle measures 70°.

The angle directly opposite it also measures 70° because vertical angles are congruent.

Intersecting lines always create two pairs of equal vertical angles—even when the lines aren’t perpendicular.

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