Four candidates $A, B, C, D$ have applied for the assignment to coach a school cricket team. If $A$ is twice as likely to be selected as $B$ , and $B$ and $C$ are given about the same chance of being selected, while $C$ is twice as likely to be selected as $D$ , what are the probabilities that:

(a) C will be selected?

(b) A will not be selected?

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Payal Gupta | Contributor-Level 10

9 months ago

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

$\begin{array}{l} G i v e n t h a t A i s t w i c e a s l i k e l y t o b e s e l e c t e d a s B \\ i . e ., P (A) = 2 P (B) \\ a n d C i s t w i c e a s l i k e l y t o b e s e l e c t e d a s D \\ ∴ P (C) = 2 P (D) \Rightarrow P (B) = 2 P (D) \\ \Rightarrow \frac{P (A)}{2} = 2 P (D) \Rightarrow P (D) = \frac{1}{4} P (A) \\ N o w B a n d C a r e g i v e n a b o u t t h e s a m e c h a n c e \\ ∴ P (B) = P (C) \\ Since, s u m o f a l l p r o b a b i l i t i e s = 1 \\ ∴ P (A) + P (B) + P (C) + P (D) = 1 \\ \Rightarrow P (A) + \frac{P (A)}{2} + \frac{P (A)}{2} + \frac{P (A)}{4} = 1 \\ \Rightarrow 4 P (A) + 2 P (A) + 2 P (A) + P (A) = 4 \\ \Rightarrow 9 P (A) = 4 \Rightarrow P (A) = \frac{4}{9} \\ (a) P (C w i l l b e s e l e c t e d) = P (C) = P (B) = \frac{P (A)}{2} \\ = \frac{4}{9} * \frac{1}{2} = \frac{2}{9} \\ (b) P (A w i l l n o t b e s e l e c t e d) = P (A') = 1 - P (A) \\ &thi \end{array}$

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