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A box contains 4 balls numbered 1 to 4. Record a sample space using a tree diagram for the following experiments: (i) A ball is drawn and the number is recorded. Then the ball is returned and a second ball is drawn and recorded. (ii) A ball is drawn and recorded. Without replacing the first ball, the experimenter draws and records a second ball. (iii) What are the sizes of these two sample spaces?
(i) With replacement: First draw branches to 1, 2, 3, 4. Each branches to 1, 2, 3, 4. S1 = {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}. (ii) Without replacement: First draw branches to 1, 2, 3, 4. Each branches to remaining 3 numbeRead more
(i) With replacement: First draw branches to 1, 2, 3, 4. Each branches to 1, 2, 3, 4.
S1 = {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}.
(ii) Without replacement: First draw branches to 1, 2, 3, 4. Each branches to remaining 3 numbers.
S2 = {(1,2), (1,3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2), (3,4), (4,1), (4,2), (4,3)}.
(iii) Size of first sample space = 4 x 4 = 16. Size of second sample space = 4 x 3 = 12.
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/
See lessWrite 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?
(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 = 4x3/2 (red) + 3x2/2 (green) + 2x1/2 (blue) = 6 + 3 + 1 = 10. Different colors = 36 - 10 = 26. P = 26/3Read more
(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/
See lessLet us say that you have a box containing 3 red pens, 4 black pens and 2 green pens. You pick a pen (without looking) from the box and put it back. Then your friend does the same. (i) What are the possible outcomes of the pen colours? Can you draw a tree diagram representing the possible outcomes? (ii) Can you use the tree diagram to guess the probability that both you and your friend pick pens of the same colour?
Total pens = 3 Red + 4 Black + 2 Green = 9. P(R) = 3/9, P(B) = 4/9, P(G) = 2/9. (i) Possible color pairs: RR, RB, RG, BR, BB, BG, GR, GB, GG (9 color outcomes). Tree Diagram branches split from Start into R, B, G for your pick, then each branches into R, B, G for your friend's pick. (ii) Same colourRead more
Total pens = 3 Red + 4 Black + 2 Green = 9. P(R) = 3/9, P(B) = 4/9, P(G) = 2/9.
(i) Possible color pairs:
RR, RB, RG, BR, BB, BG, GR, GB, GG (9 color outcomes).
Tree Diagram branches split from Start into R, B, G for your pick, then each branches into R, B, G for your friend’s pick.
(ii) Same colour means RR, BB or GG:
P(RR) = (3/9) x (3/9) = 9/81
P(BB) = (4/9) x (4/9) = 16/81
P(GG) = (2/9) x (2/9) = 4/81
P(same colour) = (9 + 16 + 4) / 81 = 29 / 81 (approx 0.358).
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/
See lessChoose the correct option to complete the sentence: The spectators giving a ‘standing ovation’ indicates that they were _______. A. amazed B. speechless C. distracted D. thoughtful
The spectators giving a standing ovation indicates that they were thoroughly amazed and inspired by what had transpired on the track. Instead of witnessing an ordinary sprint to the line, they were treated to an astonishing act of universal compassion. Standing to applaud was the audience's spontaneRead more
The spectators giving a standing ovation indicates that they were thoroughly amazed and inspired by what had transpired on the track. Instead of witnessing an ordinary sprint to the line, they were treated to an astonishing act of universal compassion. Standing to applaud was the audience’s spontaneous tribute to honor the sheer brilliance of human empathy displayed by all nine competitors.
For more NCERT Solutions of Class 9 English Kaveri Chapter 5 Nine Gold Medals Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/english/kaveri-chapter-5/
See lessComplete the sentence appropriately: The holding of hands signifies a feeling of _______.
Holding hands signifies a deep feeling of unity, brotherhood and collective empathy. This simple yet powerful gesture shows that the athletes discarded personal ambitions to stand united with their injured peer. It represents complete emotional alignment and mutual respect, showing the world that coRead more
Holding hands signifies a deep feeling of unity, brotherhood and collective empathy. This simple yet powerful gesture shows that the athletes discarded personal ambitions to stand united with their injured peer. It represents complete emotional alignment and mutual respect, showing the world that cooperation, kindness and walking together are infinitely more valuable and meaningful than winning an individual sporting race alone.
For more NCERT Solutions of Class 9 English Kaveri Chapter 5 Nine Gold Medals Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/english/kaveri-chapter-5/
See less