Testinar Grade 7 math

Theoretical Probability

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

CH09-02 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 bag contains \(4\) red, \(5\) blue, and \(6\) green marbles. What is the theoretical probability of drawing a blue marble at random?

    1. \(\frac{1}{5}\)
    2. \(\frac{1}{3}\)
    3. \(\frac{4}{15}\)
    4. \(\frac{2}{5}\)

  2. A fair six-sided die is rolled once. What is the probability of rolling a number greater than \(4\)?

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

  3. A spinner is divided into \(4\) equal sections: Red, Yellow, Blue, and Green. What is the probability of spinning Red or Green?

    Theoretical Probability visual for G7-C09-T02-Q003
    1. \(\frac{1}{4}\)
    2. \(\frac{1}{2}\)
    3. \(\frac{1}{3}\)
    4. \(\frac{3}{4}\)

  4. A jar holds \(3\) yellow, \(4\) purple, and \(8\) orange tokens. If a token is drawn at random, what is the theoretical probability it is purple?

    1. \(\frac{4}{15}\)
    2. \(\frac{4}{12}\)
    3. \(\frac{1}{4}\)
    4. \(\frac{4}{8}\)

  5. A restaurant menu has \(12\) desserts: \(5\) chocolate, \(4\) fruit, and \(3\) cream-based. If you pick one at random, what is the probability of choosing a chocolate or cream-based dessert?

    Theoretical Probability visual for G7-C09-T02-Q005
    1. \(\frac{5}{12}\)
    2. \(\frac{8}{12}\)
    3. \(\frac{2}{3}\)
    4. \(\frac{1}{2}\)

  6. A fair coin is flipped. What is the theoretical probability of getting heads?

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

  7. A bag contains \(6\) white socks and \(4\) black socks. A sock is drawn at random. What is the probability of drawing a white sock?

    1. \(\frac{3}{5}\)
    2. \(\frac{2}{5}\)
    3. \(\frac{1}{2}\)
    4. \(\frac{4}{6}\)

  8. A box contains cards numbered \(5\) through \(14\). A card is drawn at random. What is the probability of drawing a card with a number divisible by \(3\)?

    1. \(\frac{1}{5}\)
    2. \(\frac{3}{10}\)
    3. \(\frac{2}{5}\)
    4. \(\frac{1}{3}\)
Teacher and parent reference

Answer key and explanations

  1. B. \(\frac{1}{3}\)

    Total \(=4+5+6=15\). \(P(\text{blue})=\frac{5}{15}=\frac{1}{3}\).

  2. B. \(\frac{1}{3}\)

    Favorable outcomes: \(5, 6\) (two outcomes). Total outcomes: \(6\). \(P(\text{>4})=\frac{2}{6}=\frac{1}{3}\).

  3. B. \(\frac{1}{2}\)

    Each section is \(\frac{1}{4}\). Red + Green \(= \frac{1}{4} + \frac{1}{4} = \frac{1}{2}\).

  4. A. \(\frac{4}{15}\)

    Total tokens \(= 3 + 4 + 8 = 15\). \(P(\text{purple})=\frac{4}{15}\).

  5. C. \(\frac{2}{3}\)

    Chocolate or cream-based: \(5 + 3 = 8\). \(P=\frac{8}{12}=\frac{2}{3}\).

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

    A fair coin has two equally likely outcomes: heads and tails. \(P(\text{heads})=\frac{1}{2}\).

  7. A. \(\frac{3}{5}\)

    Total socks \(= 6 + 4 = 10\). \(P(\text{white})=\frac{6}{10}=\frac{3}{5}\).

  8. B. \(\frac{3}{10}\)

    Numbers: \(5, 6, 7, 8, 9, 10, 11, 12, 13, 14\) (10 total). Divisible by \(3\): \(6, 9, 12\) (3 outcomes). \(P=\frac{3}{10}\).

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