🟣 Section A — Multiple Choice 10 × 1 = 10 marks
Q1 · MCQ
The probability of an impossible event is:
Q2 · MCQ
Which of the following cannot be the probability of an event?
Q3 · MCQ
A die is thrown once. The probability of getting a number greater than 4 is:
Q4 · MCQ
A card is drawn from a well-shuffled deck. The probability of getting a king is:
Q5 · MCQ
If P(E) = 0.05, then P(not E) is:
Q6 · MCQ
When two coins are tossed together, the number of possible outcomes is:
Q7 · MCQ
A bag has 5 red and 3 green balls. The probability of drawing a green ball is:
Q8 · MCQ
The probability of drawing a face card from a deck of 52 cards is:
Q9 · MCQ
Two dice are rolled. The number of outcomes with a sum of 7 is:
Q10 · MCQ
The sum of the probabilities of all elementary events of an experiment is:
🧩 Section B — Assertion & Reason 3 × 1 = 3 marks
Q11 · A-R
Assertion: If P(E) = 0.6 then P(not E) = 0.4.
Reason: For any event, P(E) + P(not E) = 1.
Both true, Reason explains Assertion. Since P(E) + P(Ē) = 1, P(Ē) = 1 − 0.6 = 0.4.
Q12 · A-R
Assertion: When two dice are thrown, a sum of 7 is as likely as a sum of 2.
Reason: All 36 ordered pairs are equally likely.
Assertion false, Reason true. The 36 pairs are equally likely, but sum 7 arises from 6 pairs while sum 2 from only 1, so 7 is far more likely.
Q13 · A-R
Assertion: The probability of any event can be 1.3.
Reason: Probability is always a number between 0 and 1 inclusive.
Assertion false, Reason true. Since 0 ≤ P(E) ≤ 1, a value of 1.3 is impossible.
✍️ Section C — Short Answer 12 × 2 = 24 marks
Q14 · Short
A die is rolled once. Find the probability of getting a prime number.
Primes = {2,3,5} = 3 outcomes; total = 6. P = 3/6 = 1/2.
Q15 · Short
A card is drawn from 52 cards. Find P(a red card).
Red cards = 26. P = 26/52 = 1/2.
Q16 · Short
The probability that it rains today is 0.84. What is the probability that it does not rain?
P(no rain) = 1 − 0.84 = 0.16.
Q17 · Short
Two coins are tossed simultaneously. Find P(exactly one head).
Outcomes = {HH,HT,TH,TT}. Exactly one head = {HT,TH} = 2. P = 2/4 = 1/2.
Q18 · Short
A bag contains 6 red, 4 white and 5 blue balls. Find P(a white ball).
Total = 15, white = 4. P = 4/15.
Q19 · Short
A number is selected at random from 1 to 25. Find P(a multiple of 5).
Multiples of 5 = {5,10,15,20,25} = 5. P = 5/25 = 1/5.
Q20 · Short
A card is drawn from 52 cards. Find P(a black king).
Black kings = 2 (♠, ♣). P = 2/52 = 1/26.
Q21 · Short
Two dice are thrown. Find P(getting a doublet, i.e. same number on both).
Doublets = {(1,1)…(6,6)} = 6; total = 36. P = 6/36 = 1/6.
Q22 · Short
Two coins are tossed. Find P(at least one head) using the complement.
P(no head) = P(TT) = 1/4. P(at least one head) = 1 − 1/4 = 3/4.
Q23 · Short
A letter is chosen from the word "MATHEMATICS". Find P(the letter M).
Total letters = 11; M appears 2 times. P = 2/11.
Q24 · Short
A die is rolled. Find P(a number neither divisible by 2 nor by 3).
Not divisible by 2 or 3 = {1,5} = 2. P = 2/6 = 1/3.
Q25 · Short
18 defective bulbs are in a lot of 600. One bulb is drawn. Find P(a non-defective bulb).
Non-defective = 600 − 18 = 582. P = 582/600 = 97/100.
📐 Section D — Long Answer 5 × 3 = 15 marks
Q26 · Long
Two dice are thrown together. Find the probability that the sum of the numbers is (a) 8, (b) at most 4.
Total = 36. (a) Sum 8 = {(2,6),(3,5),(4,4),(5,3),(6,2)} = 5 → P = 5/36. (b) Sum ≤ 4 = {(1,1),(1,2),(2,1),(1,3),(3,1),(2,2)} = 6 → P = 6/36 = 1/6.
Q27 · Long
One card is drawn from a deck of 52. Find P(a) a heart, (b) a face card, (c) neither an ace nor a king.
(a) Hearts = 13 → 13/52 = 1/4. (b) Face cards = 12 → 12/52 = 3/13. (c) Aces + kings = 8, so favourable = 44 → 44/52 = 11/13.
Q28 · Long
A bag contains 3 red, 5 black and 4 white balls. A ball is drawn at random. Find P(red), P(not black), and P(white or red).
Total = 12. P(red) = 3/12 = 1/4. P(not black) = 1 − 5/12 = 7/12. P(white or red) = (4+3)/12 = 7/12.
Q29 · Long
A box has cards numbered 1 to 20. One card is drawn. Find P(a prime number) and P(a perfect square).
Primes 1–20 = {2,3,5,7,11,13,17,19} = 8 → P = 8/20 = 2/5. Perfect squares = {1,4,9,16} = 4 → P = 4/20 = 1/5.
Q30 · Long
A game has 8 equally likely outcomes; 3 are wins. Find P(win), P(lose), and verify they add to 1.
P(win) = 3/8. P(lose) = 1 − 3/8 = 5/8. Check: 3/8 + 5/8 = 8/8 = 1 ✓ (complementary events).