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Q.

From a group of 50 students, two sections comprising of 20 and 30 students are formed. If Ram and Rahim are two particular students among the 50 students, then the probability that they both belong to the same section is

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a

$\frac{25}{49}$

b

$\frac{12}{23}$

c

$\frac{13}{23}$

d

$\frac{24}{49}$

answer is A.

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Detailed Solution

$n (S) = {}^{50}{C_{2}}$

E=Ram and Rahim both are same section

$\begin{array}{rcl} n (E) & = & {}^{20}{C_{2}} + {}^{30}{C_{2}} \\ P (E) & = & \frac{{}^{20}{C_{2} + {}^{30}{C_{2}}}}{{}^{50}{C_{2}}} \end{array}$

$\frac{20 \times 19 + 30 \times 29}{50 \times 49} = \frac{38 + 87}{245} = \frac{125}{245} = \frac{25}{49}$

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From a group of 50 students, two sections comprising of 20 and 30 students are formed. If Ram and Rahim are two particular students among the 50 students, then the probability that they both belong to the same section is