Testinar Grade 7 math

Finding Probabilities of Compound Events

Students will build Grade 7 mastery of finding probabilities of compound events using models, equations, and test-style reasoning.

CH09-06 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 fair coin is flipped twice. What is the probability of getting heads BOTH times?

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

  2. A fair six-sided die is rolled twice. What is the probability of rolling a 3 on the first roll AND a 5 on the second roll?

    1. \(\frac{1}{6}\)
    2. \(\frac{1}{12}\)
    3. \(\frac{1}{36}\)
    4. \(\frac{1}{18}\)

  3. A bag contains 6 white marbles and 4 black marbles. One marble is drawn at random. What is the probability it is white?

    1. \(\frac{6}{10}\)
    2. \(\frac{3}{5}\)
    3. \(\frac{4}{10}\)
    4. \(\frac{2}{5}\)

  4. Two cards are drawn from a standard 52-card deck WITH replacement. What is the probability of drawing a heart on the first draw AND a spade on the second draw?

    1. \(\frac{1}{16}\)
    2. \(\frac{1}{13}\)
    3. \(\frac{1}{4}\)
    4. \(\frac{1}{8}\)

  5. A bag contains 3 red marbles and 5 blue marbles. What is the probability of drawing a red marble first, WITHOUT replacing it, then drawing a blue marble?

    1. \(\frac{3}{8}\cdot\frac{5}{8}\)
    2. \(\frac{3}{8}\cdot\frac{4}{7}\)
    3. \(\frac{15}{56}\)
    4. \(\frac{15}{64}\)

  6. Which of the following describes mutually exclusive events?

    1. Rolling a 3 AND rolling an even number on one die roll
    2. Spinning red AND spinning blue on one spinner
    3. Drawing a heart AND drawing a face card
    4. Flipping heads AND flipping tails on one coin flip

  7. A card is drawn from a standard deck. What is the probability of drawing a king OR a queen?

    1. \(\frac{4}{52}\)
    2. \(\frac{2}{13}\)
    3. \(\frac{2}{52}\)
    4. \(\frac{1}{26}\)

  8. A number from 1 to 20 is selected at random. What is the probability of selecting a multiple of 3 OR a multiple of 5?

    1. \(\frac{6}{20}\)
    2. \(\frac{9}{20}\)
    3. \(\frac{8}{20}\)
    4. \(\frac{10}{20}\)
Teacher and parent reference

Answer key and explanations

  1. B. \(\frac{1}{4}\)

    \(P(H)\cdot P(H)=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}\).

  2. C. \(\frac{1}{36}\)

    \(P(3)\cdot P(5)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36}\) for independent events.

  3. B. \(\frac{3}{5}\)

    Total marbles: 10. White marbles: 6. Probability: \(\frac{6}{10}=\frac{3}{5}\).

  4. A. \(\frac{1}{16}\)

    With replacement: \(P(\text{heart})\cdot P(\text{spade})=\frac{1}{4}\cdot\frac{1}{4}=\frac{1}{16}\).

  5. C. \(\frac{15}{56}\)

    Without replacement: \(P(\text{red first})=\frac{3}{8}\), then \(P(\text{blue second})=\frac{5}{7}\) (only 7 left). Product: \(\frac{3}{8}\cdot\frac{5}{7}=\frac{15}{56}\).

  6. D. Flipping heads AND flipping tails on one coin flip

    Mutually exclusive events cannot happen at the same time. A coin cannot show both heads and tails on one flip.

  7. B. \(\frac{2}{13}\)

    King OR Queen: \(P(\text{King})+P(\text{Queen})=\frac{4}{52}+\frac{4}{52}=\frac{8}{52}=\frac{2}{13}\) (mutually exclusive).

  8. B. \(\frac{9}{20}\)

    Multiples of 3: {3, 6, 9, 12, 15, 18} and multiples of 5: {5, 10, 15, 20}. Total: {3, 5, 6, 9, 10, 12, 15, 18, 20} = 9 numbers. So \(\frac{9}{20}\).

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