Basic Definitions — Practice Quiz

A Probability cheat sheet for Basic Definitions — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Probability of Event E

$$P(E) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$$

Probability Range

$$0 \leq P(E) \leq 1$$

Certain and Impossible Events

$$P(\text{certain event}) = 1, \quad P(\text{impossible event}) = 0$$

Complement Rule

$$P(E^c) = 1 - P(E)$$

Where: \(E^c\) = complement of E

Practice quiz

  1. A bag contains $5$ red marbles, $3$ blue marbles, and $2$ green marbles. If one marble is chosen at random, what is the probability that it is a blue marble?

    • $\frac{1}{10}$
    • $\frac{3}{10}$
    • $\frac{1}{2}$
    • $\frac{3}{5}$

    Answer: $\frac{3}{10}$

  2. Which of the following values cannot represent the probability of an event?

    • $0.75$
    • $0$
    • $1.05$
    • $\frac{1}{3}$

    Answer: $1.05$

  3. In a standard six-sided die roll, what is the probability of rolling a number less than $7$?

    • $0$
    • $\frac{1}{6}$
    • $\frac{5}{6}$
    • $1$

    Answer: $1$

  4. What is the probability of drawing a purple card from a standard deck of $52$ playing cards?

    • $0$
    • $\frac{1}{52}$
    • $\frac{1}{2}$
    • $1$

    Answer: $0$

  5. If the probability of a student passing an exam is $P(E) = 0.85$, what is the probability that the student will not pass the exam, $P(E^c)$?

    • $0.85$
    • $0.15$
    • $0.5$
    • $1$

    Answer: $0.15$

  6. A spinner has $4$ equal sections: red, blue, green, and yellow. What is the probability of NOT landing on red?

    • $\frac{1}{4}$
    • $\frac{1}{2}$
    • $\frac{3}{4}$
    • $1$

    Answer: $\frac{3}{4}$

  7. A class has $15$ boys and $10$ girls. If a student is chosen randomly to be the class representative, what is the probability that the chosen student is a girl?

    • $\frac{1}{5}$
    • $\frac{2}{5}$
    • $\frac{3}{5}$
    • $\frac{1}{2}$

    Answer: $\frac{2}{5}$

  8. An event has a probability of $P(E)$. Which of the following statements is always true?

    • $P(E) > 1$
    • $P(E) < 0$
    • $0 \leq P(E) \leq 1$
    • $P(E) = 0.5$

    Answer: $0 \leq P(E) \leq 1$

  9. A box contains $8$ apples and $4$ oranges. If one fruit is picked at random, what is the probability that it is NOT an apple?

    • $\frac{2}{3}$
    • $\frac{1}{3}$
    • $\frac{1}{2}$
    • $\frac{1}{4}$

    Answer: $\frac{1}{3}$

  10. A deck of $30$ cards is numbered from $1$ to $30$. If a card is drawn at random, what is the probability that the number on the card is NOT a multiple of $5$?

    • $\frac{1}{5}$
    • $\frac{2}{5}$
    • $\frac{3}{5}$
    • $\frac{4}{5}$

    Answer: $\frac{4}{5}$

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