A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that:

(a) All the three balls are white.

(b) All the three balls are red.

(c) One ball is red and two balls are white.

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Payal Gupta | Contributor-Level 10

8 months ago

This is a long answer type question as classified in NCERT Exemplar

$\begin{array}{l} G i v e n t h a t : N u m b e r o f r e d b a l l s = 8 \\ N u m b e r o f w h i t e b a l l s = 5 \\ (a) P (a l l t h e t h r e e b a l l s a r e w h i t e) \\ = \frac{{}_{5}{C_{3}}}{{}_{13}{C_{3}}} = \frac{\frac{5!}{3! 2!}}{\frac{13!}{3! 10!}} = \frac{5!}{3! 2!} * \frac{3! 10!}{13!} \\ = \frac{5!}{2!} * \frac{10!}{13 * 12 * 11 * 10!} \\ = \frac{5 * 4 * 3 * 2!}{2!} * \frac{1}{13 * 12 * 11} = \frac{5 * 4 * 3}{13 * 12 * 11} = \frac{5}{143} \\ (b) P (a l l t h e t h r e e b a l l s a r e r e d) \\ = \frac{{}_{8}{C_{3}}}{{}_{13}{C_{3}}} = \frac{\frac{8!}{3! 5!}}{\frac{13!}{3! 10!}} = \frac{8!}{3! 5!} * \frac{3! 10!}{13!} \\ = \frac{8 * 7 * 6 * 5!}{5!} * \frac{10!}{13 * 12 * 11 * 10!} \\ = \frac{8 * 7 * 6}{13 * 12 * 11} = \frac{28}{143} \\ (c) P (o n e b a l l i s r e d a n d t w o b a l l s a r e w h i t e) \\ = \frac{{}_{8}{C_{1}} * {}_{5}{C_{2}}}{{}_{13}{C_{3}}} = \frac{\frac{8!}{7! 1!} * \frac{5!}{2! 3!}}{\frac{13!}{3! 10!}} = \frac{8 * 7!}{7!} * \frac{5 * 4 * 3 * 2!}{2! * 3!} * \frac{3! * 10!}{13 * 12 * 11 * 10!} \\ = \frac{8 * 5}{13 * 11} = \frac{40}{143} \end{array}$

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$g (x) = {\begin{matrix} x, & x \in [0, 1) \\ - x, & x \in (- 3, 0) \end{matrix}$ 

The range of fog(x) is

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Range of fog(x) is [0, 1]

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A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that: (a) All the three balls are white. (b) All the three balls are red. (c) One ball is red and two balls are white.

Similar Questions for you

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Maths NCERT Exemplar Solutions Class 11th Chapter Sixteen 2025

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A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that:

(a) All the three balls are white.

(b) All the three balls are red.

(c) One ball is red and two balls are white.