1. Core Focus on Ratios, Rates and Statistics
Lesson 3.7
Core Focus on Ratios, Rates and Statistics
Theoretical Probability

2. Warm-Up
1. There is a 30% chance of snow. Write this probability as a fraction in simplest form and a decimal. 2. Duane practiced fielding fly balls. He caught 8 of the 10 baseballs his coach hit toward him. What is the experimental probability Duane will catch the next fly ball the coach hits toward him? 3. Find 15% of 60. 9

3. Theoretical Probability
Lesson 3.7
Theoretical Probability
Find and interpret the theoretical probability of an event.

4. Explore! Sum of Two Number Cubes
Step 1 Copy and complete the chart below. It shows the possible outcomes of one number cube across the top, and a second down the left column. The corresponding sums are shown in the table. Fill in the missing sums.
a. How many sums are shown in the chart?
b. Find and record the frequency of each sum (the number of times each sum appears).
Step 2 Copy and complete the table below to find the probability of rolling each sum on this chart.
For example, to find the probability of rolling a 7, find:

5. Explore! Sum of Two Number Cubes
Step 3 Which sum is most likely to occur?
Step 4 Roll two number cubes 36 times. Copy the table and record the sums with tally marks.
Step 5 Find the experimental probability of rolling a sum of 7 on your next turn. Does your experimental probability match the probability in Step 2? Explain your reasoning.

6. Vocabulary
Theoretical Probability The ratio of favorable outcomes to the number of possible outcomes. Complements Two probabilities whose sum is 1. Together they make up all the possible outcomes without repeating any outcomes.

7. Example 1 a. Find P(tails) when flipping a coin.
b. Find P(3 or 5) when rolling one number cube.
c. Find P(not 6) when rolling one number cube.

8. Theoretical Probability

9. Example 2
Each letter from the word MATHEMATICS is written on a separate card. A card is chosen at random. Find the probability of each event. a. P(C) b. P(M) c. P(not M) d. P(vowel)

10. Communication Prompt
What are the similarities and differences between experimental probability and theoretical probability?

11. Exit Problems
Paco played a game with 16 cards numbered 1 through 16. The cards were shuffled and one was picked at random from the complete deck. Find the probability of each event as a fraction in simplest form. a. P(10) b. P(even number) c. P(2, 3, 4, or 5) d. P(20)
Wayne has a bag of 30 marbles. Five of the marbles are red. He randomly chose a marble from the bag. find P(not red) for the marble he chose.