1. **Problem:** Find $P(\text{yellow, then red})$ when choosing markers with replacement. 2. **Formula:** For independent events with replacement, $P(A \text{ then } B) = P(A) \times P(B)$. 3. **Step 1:** Total markers = $9 + 5 + 14 + 8 = 36$. 4. **Step 2:** Calculate $P(\text{yellow}) = \frac{14}{36} = \frac{7}{18}$. 5. **Step 3:** Calculate $P(\text{red}) = \frac{9}{36} = \frac{1}{4}$. 6. **Step 4:** Calculate $P(\text{yellow, then red}) = \frac{7}{18} \times \frac{1}{4} = \frac{7}{72}$. 7. **Step 5:** Decimal: $\frac{7}{72} \approx 0.0972$. 8. **Step 6:** Percent: $0.0972 \times 100 = 9.72\%$. 1. **Problem:** Find $P(\text{blue, then green})$. 2. **Step 1:** $P(\text{blue}) = \frac{5}{36}$. 3. **Step 2:** $P(\text{green}) = \frac{8}{36} = \frac{2}{9}$. 4. **Step 3:** $P(\text{blue, then green}) = \frac{5}{36} \times \frac{2}{9} = \frac{10}{324} = \frac{5}{162}$. 5. **Step 4:** Decimal: $\frac{5}{162} \approx 0.0309$. 6. **Step 5:** Percent: $3.09\%$. 1. **Problem:** Find $P(\text{both yellow})$. 2. **Step 1:** $P(\text{yellow}) = \frac{7}{18}$. 3. **Step 2:** $P(\text{both yellow}) = \left(\frac{7}{18}\right)^2 = \frac{49}{324}$. 4. **Step 3:** Decimal: $\frac{49}{324} \approx 0.1512$. 5. **Step 4:** Percent: $15.12\%$. 1. **Problem:** Spinner with 12 equal sectors: star, heart, circle, diamond repeated 3 times; half shaded, half unshaded. 2. **Step 1:** Each sector probability = $\frac{1}{12}$. 3. **Step 2:** Find $P(\text{diamond}) = \frac{3}{12} = \frac{1}{4}$. 4. **Step 3:** Find $P(\text{circle}) = \frac{3}{12} = \frac{1}{4}$. 5. **Step 4:** $P(\text{diamond, then circle}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$. 6. **Step 5:** Decimal: $0.0625$. 7. **Step 6:** Percent: $6.25\%$. 1. **Problem:** Find $P(\text{both not stars})$. 2. **Step 1:** $P(\text{star}) = \frac{3}{12} = \frac{1}{4}$. 3. **Step 2:** $P(\text{not star}) = 1 - \frac{1}{4} = \frac{3}{4}$. 4. **Step 3:** $P(\text{both not stars}) = \left(\frac{3}{4}\right)^2 = \frac{9}{16}$. 5. **Step 4:** Decimal: $0.5625$. 6. **Step 5:** Percent: $56.25\%$. 1. **Problem:** Find $P(\text{shaded, then heart})$. 2. **Step 1:** Half sectors shaded: $\frac{6}{12} = \frac{1}{2}$. 3. **Step 2:** $P(\text{heart}) = \frac{3}{12} = \frac{1}{4}$. 4. **Step 3:** $P(\text{shaded, then heart}) = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$. 5. **Step 4:** Decimal: $0.125$. 6. **Step 5:** Percent: $12.5\%$. 1. **Problem:** Find $P(\text{both unshaded})$. 2. **Step 1:** $P(\text{unshaded}) = \frac{6}{12} = \frac{1}{2}$. 3. **Step 2:** $P(\text{both unshaded}) = \left(\frac{1}{2}\right)^2 = \frac{1}{4}$. 4. **Step 3:** Decimal: $0.25$. 5. **Step 4:** Percent: $25\%$. 1. **Problem:** Bag with slips numbered 1-20 and letters in PENNSYLVANIA. 2. **Step 1:** Total slips = 20. 3. **Step 2:** Letters in PENNSYLVANIA: P, E, N, N, S, Y, L, V, A, N, I, A. 4. **Step 3:** Vowels: E, A, A, I (4 vowels). 5. **Step 4:** Consonants: P, N, N, S, Y, L, V, N (8 consonants). 8. **Find $P(\text{less than 15, then a vowel})$** - Numbers less than 15: 14 slips. - $P(\text{less than 15}) = \frac{14}{20} = \frac{7}{10}$. - $P(\text{vowel}) = \frac{4}{12} = \frac{1}{3}$. - $P = \frac{7}{10} \times \frac{1}{3} = \frac{7}{30}$. - Decimal: $0.2333$. - Percent: $23.33\%$. 9. **Find $P(\text{multiple of 4, then V})$** - Multiples of 4: 4, 8, 12, 16, 20 (5 slips). - $P(\text{multiple of 4}) = \frac{5}{20} = \frac{1}{4}$. - $P(\text{V}) = \frac{1}{12}$. - $P = \frac{1}{4} \times \frac{1}{12} = \frac{1}{48}$. - Decimal: $0.0208$. - Percent: $2.08\%$. 10. **Find $P(\text{at least 11, then N})$** - Numbers at least 11: 11 to 20 (10 slips). - $P(\text{at least 11}) = \frac{10}{20} = \frac{1}{2}$. - $P(\text{N}) = \frac{3}{12} = \frac{1}{4}$. - $P = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$. - Decimal: $0.125$. - Percent: $12.5\%$. 11. **Find $P(\text{prime number, then consonant})$** - Prime numbers between 1 and 20: 2, 3, 5, 7, 11, 13, 17, 19 (8 slips). - $P(\text{prime}) = \frac{8}{20} = \frac{2}{5}$. - $P(\text{consonant}) = \frac{8}{12} = \frac{2}{3}$. - $P = \frac{2}{5} \times \frac{2}{3} = \frac{4}{15}$. - Decimal: $0.2667$. - Percent: $26.67\%$.