SATHEE: Probability 3 Question 15

Probability 3 Question 15

15. If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black balls will be drawn, is

(a) $\frac{13}{32}$

(b) $\frac{1}{4}$

(d) $\frac{3}{16}$

(1998, 2M)

Show Answer

Solution:

$P (2$ white and 1 black $) = P (W_{1} W_{2} B_{3}$ or $W_{1} B_{2} W_{3}$ or

$\begin{aligned} = & P (W_{1} W_{2} B_{3}) + P (W_{1} B_{2} W_{3}) + P (B_{1} W_{2} W_{3}) \\ = & P (W_{1}) P (W_{2}) P (B_{3}) + P (W_{1}) P (B_{2}) P (W_{3}) \\ + P (B_{1}) P (W_{2}) P (W_{3}) \\ = \frac{3}{4} \cdot \frac{2}{4} \cdot \frac{3}{4} + \frac{3}{4} \cdot \frac{2}{4} \cdot \frac{1}{4} + \frac{1}{4} \cdot \frac{2}{4} \cdot \frac{1}{4} = & \frac{1}{32} (9 + 3 + 1) = \frac{13}{32} \end{aligned}$

$B_{1} W_{2} W_{3})$

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Probability 3 Question 15

15. If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black balls will be drawn, is

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