1. **Problem 4a:** Find the complement probability $P(A^c)$ given $P(A) = 0.0175$. The complement rule states: $$P(A^c) = 1 - P(A)$$ Calculate: $$P(A^c) = 1 - 0.0175 = 0.9825$$ 2. **Problem 4b:** Given 61% believe life exists elsewhere, find the probability someone does *not* believe. Using complement rule: $$P(\text{not believe}) = 1 - 0.61 = 0.39$$ 3. **Problem 5:** Find probability of selecting a pea with a green pod or a white flower. From Table 3-2: - Green pod with purple flower: 5 - Green pod with white flower: 3 - Yellow pod with white flower: 2 Total peas = 5 + 3 + 4 + 2 = 14 Number with green pod = 5 + 3 = 8 Number with white flower = 3 + 2 = 5 Use formula for union: $$P(\text{green pod} \cup \text{white flower}) = P(\text{green pod}) + P(\text{white flower}) - P(\text{green pod} \cap \text{white flower})$$ Calculate probabilities: $$P(\text{green pod}) = \frac{8}{14}$$ $$P(\text{white flower}) = \frac{5}{14}$$ $$P(\text{green pod} \cap \text{white flower}) = \frac{3}{14}$$ So: $$P = \frac{8}{14} + \frac{5}{14} - \frac{3}{14} = \frac{10}{14} = \frac{5}{7} \approx 0.7143$$ 4. **Problem 6:** Find probability of selecting a pea with a yellow pod or a purple flower. From Table 3-2: - Yellow pod with purple flower: 4 - Green pod with purple flower: 5 Number with yellow pod = 4 + 2 = 6 Number with purple flower = 5 + 4 = 9 Intersection (yellow pod and purple flower) = 4 Calculate probabilities: $$P(\text{yellow pod}) = \frac{6}{14}$$ $$P(\text{purple flower}) = \frac{9}{14}$$ $$P(\text{yellow pod} \cap \text{purple flower}) = \frac{4}{14}$$ Use union formula: $$P = \frac{6}{14} + \frac{9}{14} - \frac{4}{14} = \frac{11}{14} \approx 0.7857$$ 5. **Problem 7:** Probability birthday is *not* October 18. There are 365 days in a year (ignoring leap years). Probability birthday is October 18: $$P = \frac{1}{365}$$ Probability birthday is not October 18: $$P = 1 - \frac{1}{365} = \frac{364}{365} \approx 0.9973$$ 6. **Problem 8:** Probability birthday is *not* in October. October has 31 days. Probability birthday in October: $$P = \frac{31}{365}$$ Probability birthday not in October: $$P = 1 - \frac{31}{365} = \frac{334}{365} \approx 0.9151$$