Simple Probability & Complements - Pre Algebra

1. A fair number cube is rolled. What is the probability of rolling an even number?

   $\frac{1}{2}$. Three of the six outcomes (2, 4, 6) are even.

2. A fair number cube is rolled. What is the probability of not rolling a 6?

   $\frac{5}{6}$. $1 - \frac{1}{6} = \frac{5}{6}$.

3. What is the sum of the probabilities of all the outcomes in a sample space?

   $1$. Some outcome in the sample space is certain to occur.

4. If $P(A) = \frac{2}{7}$, what is $P(\text{not } A)$?

   $\frac{5}{7}$. $1 - \frac{2}{7} = \frac{5}{7}$.

5. What is the complement of an event $A$, and how is its probability found?

   All outcomes not in $A$. $P(\text{not } A) = 1 - P(A)$.

6. A card is drawn at random from cards numbered 1 through 20. What is the probability that it is a multiple of 5?

   $\frac{1}{5}$. Four of the 20 cards (5, 10, 15, 20) are multiples of 5.

7. Two fair coins are flipped. Use the complement to find the probability of getting at least one head.

   $\frac{3}{4}$. The only outcome with no heads is TT, with probability $\frac{1}{4}$, and $1 - \frac{1}{4} = \frac{3}{4}$.

8. A bag has 3 red, 5 blue and 2 green marbles. What is the probability of drawing a blue marble at random?

   $\frac{1}{2}$. Five of the 10 marbles are blue.

9. A spinner has 8 equal sections numbered 1 through 8. What is the probability of spinning a number greater than 5?

   $\frac{3}{8}$. Three of the eight numbers (6, 7, 8) are greater than 5.

10. The probability of rain tomorrow is $0.35$. What is the probability that it does not rain?

    $0.65$. $1 - 0.35 = 0.65$.

11. A bag has 4 red marbles and 6 marbles of other colors. What is the probability of drawing a marble that is not red?

    $\frac{3}{5}$. Six of the 10 marbles are not red, and $\frac{6}{10} = \frac{3}{5}$.

12. How is the probability of an event found when all outcomes are equally likely?

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

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