Testinar Grade 7 math

Probability Models

Students will build Grade 7 mastery of probability models using models, equations, and test-style reasoning.

CH09-04 Probability
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A spinner has \(4\) equal sections labeled \(1, 2, 3, 4\). Which statement is FALSE for this uniform probability model?

    1. \(P(1)=\frac{1}{4}\)
    2. \(P(\text{odd})=\frac{1}{2}\)
    3. \(P(\text{greater than }2)=\frac{1}{2}\)
    4. \(P(5)=\frac{1}{4}\)

  2. A spinner has \(8\) equal sections: \(4\) red, \(2\) blue, \(1\) green, \(1\) yellow. What is \(P(\text{red})\) for this uniform model?

    1. \(\frac{1}{8}\)
    2. \(\frac{1}{4}\)
    3. \(\frac{1}{2}\)
    4. \(\frac{3}{4}\)

  3. Which spinner represents a non-uniform probability model?

    Probability Models visual for G7-C09-T04-Q003
    1. Left spinner only
    2. Right spinner only
    3. Both spinners
    4. Neither spinner

  4. A bag contains \(3\) red marbles, \(5\) blue marbles, and \(2\) green marbles. Which probability is correct?

    1. \(P(\text{blue})=\frac{2}{10}\)
    2. \(P(\text{red})=\frac{3}{10}\)
    3. \(P(\text{green})=\frac{1}{2}\)
    4. \(P(\text{not red})=\frac{6}{10}\)

  5. A spinner is divided into \(6\) equal sections labeled \(A, A, B, C, C, C\). What is \(P(C)\)?

    1. \(\frac{1}{2}\)
    2. \(\frac{1}{3}\)
    3. \(\frac{1}{6}\)
    4. \(\frac{2}{3}\)

  6. A weather model predicts: \(P(\text{rain})=0.3\), \(P(\text{cloudy})=0.5\), \(P(\text{sunny})=0.2\). Which statement is true?

    1. This is a valid non-uniform probability model.
    2. This is a valid uniform probability model.
    3. The probabilities do not sum to \(1\).
    4. \(P(\text{not sunny})=0.3\).

  7. Does this table represent a valid probability model?

    Probability Models visual for G7-C09-T04-Q007
    1. No, Yellow's probability is too small.
    2. No, the probabilities do not sum to \(1\).
    3. Yes, all probabilities are between \(0\) and \(1\).
    4. No, Red's probability is too large.

  8. A card is drawn from a standard deck of \(52\) cards. What is \(P(\text{King})\)?

    1. \(\frac{1}{52}\)
    2. \(\frac{1}{13}\)
    3. \(\frac{1}{4}\)
    4. \(\frac{1}{2}\)
Teacher and parent reference

Answer key and explanations

  1. D. \(P(5)=\frac{1}{4}\)

    \(5\) is not on the spinner, so \(P(5)=0\). The others are correct.

  2. C. \(\frac{1}{2}\)

    There are \(4\) red sections out of \(8\) total, so \(P(\text{red})=\frac{4}{8}=\frac{1}{2}\).

  3. B. Right spinner only

    The left spinner has equal sections (uniform). The right spinner has unequal sectors: one 60°, one 120°, one 180° (non-uniform).

  4. B. \(P(\text{red})=\frac{3}{10}\)

    Total marbles: \(3+5+2=10\). Red: \(3\) out of \(10\) gives \(\frac{3}{10}\). (Blue would be \(\frac{5}{10}\), green \(\frac{2}{10}\), not red \(\frac{7}{10}\)).

  5. A. \(\frac{1}{2}\)

    There are \(3\) sections labeled \(C\) out of \(6\) equal sections, so \(P(C)=\frac{3}{6}=\frac{1}{2}\).

  6. A. This is a valid non-uniform probability model.

    \(0.3 + 0.5 + 0.2 = 1\), so probabilities sum to \(1\) (valid). Outcomes have different probabilities (non-uniform). Also, \(P(\text{not sunny})=0.3+0.5=0.8\).

  7. C. Yes, all probabilities are between \(0\) and \(1\).

    \(0.4 + 0.35 + 0.25 = 1.0\) and each probability is in \([0, 1]\), so this is valid.

  8. B. \(\frac{1}{13}\)

    There are \(4\) Kings in \(52\) cards, so \(P(\text{King})=\frac{4}{52}=\frac{1}{13}\).

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