With replacement, tree branches into 4 paths then 4 paths each, creating 16 pairs (size 16). Without replacement, first draw branches into 4 paths then 3 paths each, creating 12 pairs (size 12).
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?
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(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)
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