Ans: (a) (i) Class $A$: $21\text{ marks}$, class $B$: $14\text{ marks}$ (ii) class $B$ (b) (i) $\dfrac{297}{700}$ (ii) $\dfrac{1\ 089}{4\ 900}$ (iii) $\dfrac{11}{21}$
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- The inter-quartile range of the score distribution of class $A$
$\begin{array}{cl}
= & 39 – 18 \\
= & 21 \text{ marks}
\end{array}$The inter-quartile range of the score distribution of class $B$
$\begin{array}{cl}
= & 25 – 11 \\
= & 14 \text{ marks}
\end{array}$ - Since the inter-quartile range of the score distribution of class $B$ is smaller than that of class $A$, then class $B$ is less dispersed than class $A$.
- The inter-quartile range of the score distribution of class $A$
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- P(exactly 2 pass)
$\begin{array}{cl}
= & \dfrac{C^{28}_2 \times C^{22}_1}{C^{50}_3}\\
= & \dfrac{297}{700}
\end{array}$ - P(exactly 2 pass and in the same class)
$\begin{array}{cl}
= & \dfrac{C^{18}_2\times C^{22}_1}{C^{50}_3} + \dfrac{C^{10}_2\times C^{22}_1}{C^{50}_3} \\
= & \dfrac{1089}{4900}
\end{array}$ - P(in the same class | exactly 2 pass)
$\begin{array}{cl}
= & \dfrac{\text{P(exactly 2 pass and in the same class)}}{\text{P(exactly 2 pass)}} \\
= & \dfrac{\frac{1089}{4900}}{\frac{297}{700}} \\
= & \dfrac{11}{21}
\end{array}$
- P(exactly 2 pass)
