Question

If a committee of $3$ to be chosen from a group of $38$ people of which you are a member. What is the probability that you will be on the committee

• A. ${}^{38}C_3$
• B. ${}^{37}C_2$
• C. $\frac{{}^{37}C_2}{{}^{38}C_3}$
• D. $\frac{666}{8436}$

Answer 1

The correct option is C

$\frac{{}^{37}C_2}{{}^{38}C_3}$

Find the required probability:

The probability of choosing the committee from the group of $38$ members, (Total cases) $n\left(S\right)={}^{38}C_3$

The probability that you are in the chosen committee, (Favorable cases) $n\left(E\right)={}^{37}C_2$

$\therefore$The required probability, $\mathit{P}\mathbf{\left(}\mathit{E}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{n}\mathbf{\left(}\mathbf{E}\mathbf{\right)}}{\mathbf{n}\mathbf{\left(}\mathbf{S}\mathbf{\right)}}$

$=\frac{{}^{37}\mathrm{C}_2}{{}^{38}\mathrm{C}_3}$

Hence, Option ‘C’ is Correct.