Section A (1 Mark each)
Q1. (c) $\frac{31}{36}$
Total pens = 144. Defective = 20. Good = $144 - 20 = 124$.
$P(\text{Buy}) = P(\text{Good}) = \frac{124}{144} = \frac{31}{36}$.
Q2. (b) $\frac{1}{3}$
Total faces = 6. Faces with 'A' = 2.
$P(A) = \frac{2}{6} = \frac{1}{3}$.
Q3. (b) $0.7$
$P(\text{Lose}) = 1 - P(\text{Win}) = 1 - 0.3 = 0.7$.
Q4. (a) Both A and R are true and R is the correct explanation of A.
Getting a number > 6 on a standard die is impossible. Probability is 0.
Section B (2 Marks each)
Q5. A leap year has 366 days = 52 weeks + 2 days.
The remaining 2 days can be: (Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri),
(Fri, Sat), (Sat, Sun).
Total outcomes = 7. Favorable (contains Sunday) = 2 {(Sun, Mon), (Sat, Sun)}.
Probability = $\frac{2}{7}$.
Q6. Total marbles = $5 + 8 + 4 = 17$.
(i) $P(\text{Red}) = \frac{5}{17}$.
(ii) $P(\text{Not Green}) = \frac{5+8}{17} = \frac{13}{17}$.
Q7. Word: ASSOCIATION. Total letters = 11.
Vowels: A, O, I, A, I, O (6 vowels).
$P(\text{Vowel}) = \frac{6}{11}$.
Section C (3 Marks each)
Q8. Total marbles = 24. Let green marbles = $g$.
$P(\text{Green}) = \frac{g}{24} = \frac{2}{3} \Rightarrow g = 16$.
Blue marbles = Total - Green = $24 - 16 = 8$.
Q9. Total outcomes for 3 tosses = 8: {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.
Hanif wins if {HHH, TTT}. Favorable outcomes for winning = 2.
Hanif loses if outcome is NOT {HHH, TTT}. Favorable outcomes for losing = $8 - 2 = 6$.
$P(\text{Lose}) = \frac{6}{8} = \frac{3}{4}$.
Section D (5 Marks)
Q10. Total balls initially = 12. Black balls = $x$.
(i) $P_1(\text{Black}) = \frac{x}{12}$.
(ii) 6 more black balls added. New Total = $12 + 6 = 18$. New Black = $x + 6$.
$P_2(\text{Black}) = \frac{x+6}{18}$.
Given $P_2 = 2 \times P_1$:
$\frac{x+6}{18} = 2 \times \frac{x}{12}$
$\frac{x+6}{18} = \frac{x}{6}$
$x + 6 = 3x \Rightarrow 2x = 6 \Rightarrow x = 3$.
Section E (Case Study - 4 Marks)
(i) Total coins = $100 \text{ (50p)} + 50 \text{ (₹1)} + 20 \text{ (₹2)} + 10 \text{ (₹5)} = 180$.
(ii) $P(50p) = \frac{100}{180} = \frac{5}{9}$.
(iii) $P(\text{Not ₹5}) = 1 - P(₹5)$.
$P(₹5) = \frac{10}{180} = \frac{1}{18}$.
$P(\text{Not ₹5}) = 1 - \frac{1}{18} = \frac{17}{18}$.