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Home » Four candidates A, B, C, D have applied for the assignment to coach a school cricket team. If A is nd C are given about the same chance of being selected, D, what are the probabilities that (a) C will be selected? (b) A will not be selected?
Four candidates A, B, C, D have applied for the assignment to coach a school cricket team. If A is nd C are given about the same chance of being selected, D, what are the probabilities that
(a) C will be selected?
(b) A will not be selected?
CBSE | Class 11 | Maths | NCERT Exemplar | Probability
Four candidates A, B, C, D have applied for the assignment to coach a school cricket team. If A is nd C are given about the same chance of being selected, D, what are the probabilities that
(a) C will be selected?
(b) A will not be selected?

Solution:
It is given that A is twice as likely to be selected as B
that is P(A)=2 P(B) \ldots \ldots 1
and C is twice as likely to be selected as D.
that is P(C)=2 P(D) \ldots \ldots 2
So now, B and \mathrm{C} are given about the same chance
As, the sum of all probabilities =1
\begin{array}{l} \therefore P(A)+P(B)+P(C)+P(D)=1 \\ \Rightarrow P(A)+P(B)+P(B)+P(D)=1[\text { from } 3] \end{array}
\begin{array}{l} \Rightarrow \mathrm{P}(\mathrm{A})+\frac{\mathrm{P}(\mathrm{A})}{2}+\frac{\mathrm{P}(\mathrm{A})}{2}+\frac{\mathrm{P}(\mathrm{C})}{2}=1 (\mathrm{from} 1 \& 2] \\ \Rightarrow \frac{{2 \mathrm{P(A)}}+{P}(\mathrm{A})+\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})}{2}=1 [\text { from } 3]\\ \Rightarrow 4 \mathrm{P}(\mathrm{A})+\frac{\mathrm{P}(\mathrm{A})}{2}=2[\text { from } 1] \\ \Rightarrow \frac{8 \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{A})}{2}=2 \\ \Rightarrow 9 \mathrm{P}(\mathrm{A})=4 \\ \Rightarrow \mathrm{P}(\mathrm{A})=\frac{4}{9} \end{array}
(a) P(C will be selected )=P(C)
=P(B)[ from 3]
=\frac{\mathrm{P}(\mathrm{A})}{2}[\text { from 1] }
=\frac{4}{9} \times \frac{1}{2}=\frac{2}{9}
(b) P (A will not be selected) =P\left(A^{\prime}\right)
Using the compliment rule
=1-\mathrm{P}(\mathrm{A})
=1-\frac{4}{9}
=\frac59

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