Section A (1 Mark each)
Q1. (a) 0.93
$P(\text{not } E) = 1 - P(E) = 1 - 0.07 = 0.93$.
Q2. (b) $-1.5$
Probability of an event cannot be negative. It always lies between 0 and 1 (inclusive).
Q3. (c) 0
The probability of an impossible event is 0.
Q4. (a) Both A and R are true and R is the correct explanation of A.
Prime numbers on a die are 2, 3, 5. Total outcomes = 6.
$P(\text{Prime}) = \frac{3}{6} = \frac{1}{2}$. Reason correctly explains the calculation.
Section B (2 Marks each)
Q5. Total outcomes when tossing a coin twice: {HH, HT, TH, TT} = 4.
Favorable outcomes (at least one head): {HH, HT, TH} = 3.
Probability = $\frac{3}{4}$.
Q6. Total balls = $3 \text{ (Red)} + 5 \text{ (Black)} = 8$.
(i) $P(\text{Red}) = \frac{3}{8}$.
(ii) $P(\text{Not Red}) = 1 - P(\text{Red}) = 1 - \frac{3}{8} = \frac{5}{8}$.
Q7. Total outcomes on a die = 6 {1, 2, 3, 4, 5, 6}.
(i) Odd numbers: {1, 3, 5}. Count = 3. $P(\text{Odd}) = \frac{3}{6} = \frac{1}{2}$.
(ii) Number between 2 and 6: {3, 4, 5}. Count = 3. $P(\text{Between 2 and 6}) = \frac{3}{6}
= \frac{1}{2}$.
Section C (3 Marks each)
Q8. Total cards = 52.
(i) King of red color: (King of Hearts, King of Diamonds) = 2. $P = \frac{2}{52} =
\frac{1}{26}$.
(ii) Face card: (4 Jacks, 4 Queens, 4 Kings) = 12. $P = \frac{12}{52} = \frac{3}{13}$.
(iii) A spade: 13 cards. $P = \frac{13}{52} = \frac{1}{4}$.
Q9. Total outcomes when two dice are thrown = $6 \times 6 = 36$.
Favorable outcomes for sum = 8:
{(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}.
Number of favorable outcomes = 5.
Probability = $\frac{5}{36}$.
Section D (5 Marks)
Q10. Total discs = 90.
(i) Two-digit numbers (10 to 90): Count = $90 - 10 + 1 = 81$.
$P(\text{Two-digit}) = \frac{81}{90} = \frac{9}{10}$.
(ii) Perfect square numbers: {1, 4, 9, 16, 25, 36, 49, 64, 81}. Count = 9.
$P(\text{Perfect Square}) = \frac{9}{90} = \frac{1}{10}$.
(iii) Numbers divisible by 5: {5, 10, ..., 90}. Count = 18.
$P(\text{Divisible by 5}) = \frac{18}{90} = \frac{1}{5}$.
Section E (Case Study - 4 Marks)
Q11. Total outcomes = 8 {1, 2, 3, 4, 5, 6, 7, 8}.
(i) Point at 8: Favorable = 1.
$P(8) = \frac{1}{8}$.
(ii) Point at odd number: {1, 3, 5, 7}. Favorable = 4.
$P(\text{Odd}) = \frac{4}{8} = \frac{1}{2}$.
(iii) Point at number greater than 2: {3, 4, 5, 6, 7, 8}. Favorable = 6.
$P(>2) = \frac{6}{8} = \frac{3}{4}$.