29. (a) In this part you may use this Venn diagram to help you answer the questions. In a class of 30 students, 25 study French \( (F), 18 \) study Spanush (S) One student does not study French or Spanish. (i) Find the number of students who study French and Spanish (ii) One of the 30 students is chosen at random. Find the probability that this student studies French but not Spanish. (iii) A student who does not study Spanish is chosen at random. Find the probability that this student studies Erench

Step 1 ：\(n(F \cap S) = n(F) + n(S) - n(F \cup S)\)

Step 2 ：\(n(F \cap S) = 25 + 18 - 29\)

Step 3 ：\(n(F \cap S) = 14\)

Step 4 ：\(n(F \setminus S) = n(F) - n(F \cap S)\)

Step 5 ：\(n(F \setminus S) = 25 - 14\)

Step 6 ：\(n(F \setminus S) = 11\)

Step 7 ：\(P(F \setminus S) = \frac{n(F \setminus S)}{n(U)}\)

Step 8 ：\(P(F \setminus S) = \frac{11}{30}\)

Step 9 ：\(n(\bar{S}) = n(U) - n(S)\)

Step 10 ：\(n(\bar{S}) = 30 - 18\)

Step 11 ：\(n(\bar{S}) = 12\)

Step 12 ：\(P(F | \bar{S}) = \frac{n(F \cap \bar{S})}{n(\bar{S})}\)

Step 13 ：\(P(F | \bar{S}) = \frac{11}{12}\)