7th Grade Probability and Probability Models Test Solutions and Scoring (PDF)

1. Certain; 1.
2. Equally likely; 1/2.
3. Impossible; 0.
4. Likely; 5/6.

certain, equally likely, impossible, likely

Scoring: Half a point per correct answer.

\(\frac{5}{10}=\frac{1}{2}\).

\(1-\frac{1}{2}=\frac{1}{2}\)

\(\frac{1}{2}\); \(\frac{1}{2}\)

Scoring: 1 point for each.

\(\frac{4}{30}=\frac{2}{15}\approx 0.13\).

\(\frac{1}{6}\approx 0.17\), close but not equal.

\(\frac{2}{15}\) versus \(\frac{1}{6}\)

Scoring: 1 point for the relative frequency; 1 point for the comparison.

\(x=1-0.1-0.35-0.25=0.3\).

B has the greatest probability, 0.35.

x = 0.3; B

Scoring: 1 point for x; 1 point for the most likely outcome.

About 75

Scoring: 1 point for the setup; 1 point for the answer.

\(\frac{27}{50}=0.54\) versus \(0.5\).

The difference is small, which is expected with only 50 tosses.

0.54 versus 0.5

Scoring: 1 point for the relative frequency; 1 point for the comparison.

\(1-0.82=0.18\).

\(0.18\times 500=90\)

0.18; about 90 flights

Scoring: 1 point for the probability; 1 point for the prediction.

1. \(1-0.4-0.25-0.2=0.15\).
2. \(0.4+0.25=0.65\).
3. \(0.2\times 200=40\).

Scoring: 1 point for each part.

1. \(\frac{14}{20}=0.7\).
2. \(0.7\times 30=21\) wins.
3. Each game depends on chance, so results of a few games can differ from the relative frequency.

Scoring: 1 point for each part.