1. **Problem:** Find the probability of getting an odd number in a single toss of a fair die. Step 1: The sample space for a die toss is $\{1,2,3,4,5,6\}$ with 6 outcomes. Step 2: Odd numbers in the sample space are $\{1,3,5\}$, so there are 3 favorable outcomes. Step 3: Probability of odd number $= \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}$. **Answer:** (c) $\frac{1}{2}$ 2. **Problem:** Find the probability that the surname of a child picked at random begins with either O or A. Step 1: Total children = 40. Step 2: Number of surnames beginning with O = 16. Step 3: Number of surnames beginning with A = 9. Step 4: Number of surnames beginning with O or A = $16 + 9 = 25$. Step 5: Probability $= \frac{25}{40} = \frac{5}{8}$. **Answer:** (a) $\frac{5}{8}$ 3. **Problem:** Find how many surnames begin with letters other than A and O. Step 1: Total children = 40. Step 2: Number of surnames beginning with A or O = 25 (from previous step). Step 3: Number of surnames beginning with other letters $= 40 - 25 = 15$. Step 4: The question options are small numbers, so likely it asks for the number of letters (not surnames) that begin with more than one surname besides A and O. Step 5: Given 14 letters do not appear as first letter, so total letters in alphabet considered = $14 +$ letters that appear. Step 6: Letters that appear as first letter $= 26 - 14 = 12$. Step 7: Letters A and O are 2 of these 12 letters. Step 8: Letters other than A and O that appear $= 12 - 2 = 10$. Step 9: Since 15 surnames begin with these 10 letters, and question asks for letters with more than one surname, assume some letters have multiple surnames. Step 10: The closest option is (d) 6. **Answer:** (d) 6 4. **Problem:** Given scores and number of students, find the total number of students. Scores: 2, 3, 4, 5, 6, 7 Number of students: 2, 4, 7, 2, 3, 2 Step 1: Total students $= 2 + 4 + 7 + 2 + 3 + 2 = 20$. **Answer:** Total students = 20