As per URDPFI Guidelines (2015), match the following settlement types in Group-I to their population range in Group-II.
\[ \begin{array}{|c|c|} \hline \textbf{Group I} & \textbf{Group II} \\ \hline (P)\ \text{Large city} & (1)\ 50,000 \text{ to } 1 \,\text{lakh} \\ (Q)\ \text{Metropolitan city II} & (2)\ 50 \,\text{lakh to } 1 \,\text{crore} \\ (R)\ \text{Small town II} & (3)\ 20,000 \text{ to } 50,000 \\ (S)\ \text{Medium town I} & (4)\ \text{More than 1 crore} \\ & (5)\ 5 \,\text{lakh to } 10 \,\text{lakh} \\ \hline \end{array} \]
Step 1: Large city.
As per URDPFI, a large city has a population between 5 lakh and 10 lakh.
\[
P \Rightarrow 5
\]
Step 2: Metropolitan city II.
Metropolitan cities are divided into classes, and Metropolitan II corresponds to a population range of 50 lakh to 1 crore.
\[
Q \Rightarrow 2
\]
Step 3: Small town II.
Small towns are classified by population 20,000–50,000.
\[
R \Rightarrow 3
\]
Step 4: Medium town I.
Medium towns usually range between 50,000–1 lakh.
\[
S \Rightarrow 1
\]
\[
\boxed{P-5, \ Q-2, \ R-3, \ S-1}
\]
| Group I | Group II |
| (P) Landfill site | (1) Development on previously developed site |
| (Q) Greenfield development | (2) Land to dispose solid waste |
| (R) Green Belt | (3) Development on previously undeveloped land |
| (S) Policy to protect | (4) livestock |
| (5) A buffer to control urban development |
P and Q play chess frequently against each other. Of these matches, P has won 80% of the matches, drawn 15% of the matches, and lost 5% of the matches.
If they play 3 more matches, what is the probability of P winning exactly 2 of these 3 matches?