CBSE 2025, Set 1

Question

A box has 4 green, 8 blue and 3 red pens. A student picks up a pen at random, checks its colour and replaces it in the box. He repeats this process 3 times. The probability that at least one pen picked was red is: A). $\frac{124}{125}$ B). $\frac{1}{125}$ C). $\frac{61}{125}$ D). $\frac{64}{125}$

Edvaya · Accepted Answer

The correct answer is $\frac{61}{125}$. Total number of pens = 4 (green) + 8 (blue) + 3 (red) = 15 Probability of picking a red pen, $P(R) = \frac{3}{15} = \frac{1}{5}$. Probability of not picking a red pen, $P(R') = 1 - \frac{1}{5} = \frac{4}{5}$. Since the pen is replaced each time, the events are independent. The probability of picking at least one red pen in 3 trials is: $P(	ext{at least one red}) = 1 - P(	ext{no red pen picked in all 3 trials})$ $= 1 - P(R') 	imes P(R') 	imes P(R')$ $= 1 - (\frac{4}{5})^3$ $= 1 - \frac{64}{125}$ $= \frac{125 - 64}{125} = \frac{61}{125}$

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