(i) S = {HH, HT, TH, TT}, P(at least 1 head) = 3/4.
(ii) S = {1, 2, …, 10}, P(even) = 5/10 = 1/2.
(iii) S = {1, 2, 3, 4, 5, 6}, P(> 4) = 2/6 = 1/3.
(iv) P(not red) = 3/6 = 1/2.
(v) S has 8 outcomes, P(exactly 2 heads) = 3/8.
Write the sample space and calculate the probability based on the given information. (i) Two coins are tossed at the same time. What is the probability of getting at least one head? (ii) Ten identical cards numbered 1 to 10 are placed in a box. One card is drawn at random. What is the probability of drawing a card with an even number? (iii) A die is rolled once. What is the probability of getting a number greater than 4? (iv) A bag contains 3 red balls, 2 blue balls and 1 green ball. One ball is picked at random. What is the probability that it is not red? (v) Three coins are tossed simultaneously. What is the probability of getting exactly two heads?
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(i) Total pairs = 36. Primes greater than 5 are 7 and 11: {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1), (5,6), (6,5)} (8 pairs). P = 8/36 = 2/9.
(ii) Total pairs = (9 x 8) / 2 = 36. Same color pairs = 4×3/2 (red) + 3×2/2 (green) + 2×1/2 (blue) = 6 + 3 + 1 = 10. Different colors = 36 – 10 = 26. P = 26/36 = 13/18.
(iii) S has 8 outcomes. Favourable are {HHT, HTH}. P = 2/8 = 1/4.
(iv) Total numbers = 4x3x2x1 = 24. Even ends in 2 or 4: 2 x 6 = 12. P = 12/24 = 1/2.
(v) Each question P(C) = 1/4, P(W) = 3/4. Exactly 2 correct: CCW, CWC, WCC. P = 3 x (1/4)² x (3/4) = 9/64.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 7 The Mathematics of Maybe: Introduction to Probability Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-7/
(i) S = {HH, HT, TH, TT}. Favourable = {HH, HT, TH}. P(at least 1 head) = 3/4 = 0.75.
(ii) S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Even = {2, 4, 6, 8, 10}. P(even) = 5/10 = 1/2 = 0.5.
(iii) S = {1, 2, 3, 4, 5, 6}. Favourable = {5, 6}. P(> 4) = 2/6 = 1/3.
(iv) Total balls = 3 + 2 + 1 = 6. Not red = 2 blue + 1 green = 3. P(not red) = 3/6 = 1/2 = 0.5.
(v) S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} (8 outcomes). Favourable = {HHT, HTH, THH}. P(exactly 2 heads) = 3/8 = 0.375.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 7 The Mathematics of Maybe: Introduction to Probability Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-7/