When finding $\operatorname{P}(A \text{ or } B)$ for inclusive events, why must $\operatorname{P}(A \text{ and } B)$ be subtracted from $\operatorname{P}(A) + \operatorname{P}(B)$?

To account for outcomes that are not in A or B.

Because the events are independent.

To correct for double-counting the outcomes that are in both A and B.

To make sure the probability is a positive number.

Mutually Exclusive and Inclusive Events Practice — Grade 9 math

Lesson 68: Mutually Exclusive and Inclusive Events — Practice Questions

1. In a group of 50 students, 28 are in the band and 20 are in the choir. If 9 students are in both, what is the probability that a student is in the band or the choir? (Enter as a fraction) ___
2. When finding $\operatorname{P}(A \text{ or } B)$ for inclusive events, why must $\operatorname{P}(A \text{ and } B)$ be subtracted from $\operatorname{P}(A) + \operatorname{P}(B)$?
- A. To account for outcomes that are not in A or B.
- B. Because the events are independent.
- C. To correct for double-counting the outcomes that are in both A and B.
- D. To make sure the probability is a positive number.
3. From a standard 52-card deck, what is the probability of drawing a face card (Jack, Queen, or King) or a club? (Enter as a simplified fraction) ___
4. Which of the following is the correct solution to the inequality $10 - 2x \ge 16$?
- A. x \ge -3
- B. x \le -3
- C. x \ge 3
- D. x \le 3
5. Solve the inequality for $y$: $-6y + 5 < 29$. The solution is $y >$ ___.
6. When rolling a pair of fair six-sided dice, what is the probability that the sum is 4 or 11? Express your answer as a fraction: ___.
7. From a standard 52-card deck, what is the probability of drawing a Jack or an Ace in a single draw?
- A. $\frac{1}{13}$
- B. $\frac{2}{13}$
- C. $\frac{1}{26}$
- D. $\frac{4}{13}$
8. A jar contains 6 yellow, 4 purple, and 5 orange marbles. If one marble is drawn, what is the probability it is yellow or purple? Answer as a simplified fraction: ___.
9. Which pair of events is mutually exclusive when rolling two fair six-sided dice?
- A. The sum is 10 and one die shows a 5.
- B. The sum is even and the sum is a multiple of 3.
- C. The sum is 3 and the roll is doubles.
- D. The sum is greater than 8 and one die shows a 6.
10. When rolling a pair of fair six-sided dice, what is the probability the sum is a multiple of 4 or a multiple of 5?
- A. $\frac{1}{3}$
- B. $\frac{7}{36}$
- C. $\frac{4}{9}$
- D. $\frac{1}{2}$