With replacement, total pens = 9. Outcomes for colors are RR, RB, RG, BR, BB, BG, GR, GB, GG. The probability of both picking the same color is P(RR) + P(BB) + P(GG) = 9/81 + 16/81 + 4/81 = 29/81.
Let 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?
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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/