1. Problem: Find the experimental probability of drawing red from the bar graph. The formula for experimental probability is: $$P(E) = \frac{\text{Number of times event occurs}}{\text{Total number of trials}}$$ From the graph, red is drawn 7 times out of 20 total draws. So, $$P(\text{red}) = \frac{7}{20}$$ 2. Problem: Find the experimental probability of drawing orange. From the graph, orange is drawn 3 times out of 20 draws. So, $$P(\text{orange}) = \frac{3}{20}$$ 3. Problem: Find the experimental probability of drawing not yellow. Yellow is drawn 2 times, so not yellow is drawn $20 - 2 = 18$ times. So, $$P(\text{not yellow}) = \frac{18}{20} = \frac{9}{10}$$ 4. Problem: Find the experimental probability of drawing a color with more than 4 letters in its name. Colors with more than 4 letters: green (5), yellow (6), orange (6), purple (6). Number of times drawn: - Green: 4 - Yellow: 2 - Orange: 3 - Purple: 1 Total draws for these colors: $$4 + 2 + 3 + 1 = 10$$ So, $$P(\text{color with >4 letters}) = \frac{10}{20} = \frac{1}{2}$$ 5. Problem: Expectation of boys' names out of 25 when 5 are chosen with 3 boys and 2 girls. The ratio of boys in the sample is: $$\frac{3}{5}$$ Assuming the sample is representative, expected boys in 25 names: $$25 \times \frac{3}{5} = 15$$ 6. Problem: Theoretical probability of rolling a 2 on a number cube. A number cube has 6 faces numbered 1 to 6. Probability: $$P(2) = \frac{1}{6}$$ 7. Problem: Theoretical probability of rolling a 5. Similarly, $$P(5) = \frac{1}{6}$$ 8. Problem: Theoretical probability of rolling an even number. Even numbers on cube: 2, 4, 6 (3 outcomes) So, $$P(\text{even}) = \frac{3}{6} = \frac{1}{2}$$ 9. Problem: Theoretical probability of rolling a number greater than 1. Numbers greater than 1: 2, 3, 4, 5, 6 (5 outcomes) So, $$P(>1) = \frac{5}{6}$$