Four candidates A, B, C and 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 C will be Selected?

A
1/9
B
2/9
C
5/9
D
4/9

Solution:

let the probability of D selected is x
The

$\begin{aligned} P (C) = 2 x \\ P (B) = 2 x \\ P (A) = 4 x \end{aligned}$

Now, $P (A) + P (B) + P (C) + P (D) = 1$

[sum of all probabilities is equal to one]

$\begin{array}{lr} ∴ 4 x + 2 x + 2 x + x = 1 \\ \Rightarrow 9 x = 1 \Rightarrow x = \frac{1}{9} \\ ∴ P (C selected) = 2 x = 2 \times \frac{1}{9} = \frac{2}{9} \end{array}$

Solution:

Related content