1 A quiz team of 4 students is to be selected from a group of 7 girls and 5 boys. The team is selected at random from the students in the group. The number of girls in the team is denoted by the random variable \(X\).

1. Show that \(\mathrm { P } ( X = 4 ) = \frac { 7 } { 99 }\). Table 1 shows the probability distribution of \(X\). \begin{table}[h]

   \(r\)	0	1	2	3	4
   \(\mathrm { P } ( X = r )\)	\(\frac { 1 } { 99 }\)	\(\frac { 14 } { 99 }\)	\(\frac { 42 } { 99 }\)	\(\frac { 35 } { 99 }\)	\(\frac { 7 } { 99 }\)

   \captionsetup{labelformat=empty} \caption{Table 1}
   \end{table}
2. Find each of the following.
   • \(\mathrm { E } ( X )\)
   • \(\operatorname { Var } ( X )\)
   It is decided that the quiz team must have at least 1 girl and at least 1 boy, but the team is still otherwise selected at random.
3. Explain whether \(\mathrm { E } ( X )\) would be smaller than, equal to or larger than the value which you found in part (b).