(i) Primes 7 and 11 give 8 pairs, P = 8/36 = 2/9.
(ii) P(different) = 1 – P(same) = 1 – 13/36 = 23/36.
(iii) Favourable outcomes {HHT, HTH}, P = 2/8 = 1/4.
(iv) Last digit 2 or 4, P = 12/24 = 1/2.
(v) P = 3 x (1/4)² x (3/4) = 9/64.
Write the sample space and calculate the probability based on the given information. (i) Two dice are rolled. What is the probability that the sum is a prime number greater than 5? (ii) A bag contains 4 red, 3 green, and 2 blue balls. Two balls are drawn without replacement. What is the probability that both are of different colours? (iii) Three coins are tossed. What is the probability that the first coin shows heads and exactly two heads occur in total? (iv) A four-digit number is formed using the digits 1, 2, 3, and 4 with no repetition. What is the probability that the number is even? (v) A student takes a multiple-choice test with 3 questions, each having 4 options (A, B, C, D), with only one correct answer. What is the probability that the student guesses and gets exactly 2 answers correct?
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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/