Directions (48-51): The scatter chart given below shows the number of boys on (Y – axis) and number of girls (X – axis) in three different class of P, Q and R.

NOTE: If there were 10 more girls in class R then the probability of selecting a girl from R would be 40%

Number of girls in class Q is $\frac{200}{3}$% the number of girls in class R. If the number of boys in class S is 20% more than the boys in class Q and the number of girls are same as that of Q, then find the probability of selecting two girls from class S.

Step 1: Understand the Data from the Scatter Chart

By observing the given scatter chart, the Y-axis represents the number of boys, and the X-axis represents the number of girls in classes P, Q, and R.
From the points plotted on the chart:
For Class P: Boys = 40, Girls = $a+b$
For Class Q: Boys = 20, Girls = $a+3b$
For Class R: Boys = 60, Girls = $a+5b$

Step 2: Calculate the Number of Girls in Class R

Let the number of girls in class R be $G_R$.
According to the note, if there were 10 more girls in class R, the probability of selecting a girl from class R would be 40% (or $\frac{2}{5}$).
We can write the probability equation as:
$\frac{G_R+10}{\text{Boys in R}+G_R+10}$
Substitute the number of boys in class R (60):
$\frac{G_R+10}{60+G_R+10}$
$\frac{G_R+10}{70+G_R}$
Cross-multiply and solve for $G_R$:
$5(G_R+10)=2(70+G_R)$
$5G_R+50=140+2G_R$
$3G_R=90$
$G_R=30$
So, the number of girls in class R is 30.

Step 3: Calculate the Number of Girls in Class Q

The question states that the number of girls in class Q is $\frac{200}{3}\%$ the number of girls in class R.
Number of girls in class Q ($G_Q$):
$G_Q=\frac{200}{3\times 100}\times 30$
$G_Q=\frac{2}{3}\times 30=20$
So, the number of girls in class Q is 20.

Step 4: Find the Number of Boys and Girls in Class S

For class S:
1. The number of boys is 20% more than the boys in class Q.
Boys in class Q = 20 (from the chart).
Boys in class S = $20+(20\%\text{of}20)=20+4=24$.
2. The number of girls is the same as that of class Q.
Girls in class S = 20.
Total students in class S = $24+20=44$ students.

Step 5: Find the Probability of Selecting Two Girls from Class S

The probability of selecting two girls is given by the ratio of the number of ways to select 2 girls to the total number of ways to select 2 students.
Number of ways to select 2 girls from 20 girls:
${\hspace{0.17em}}^{20}{C}_2=\frac{20\times 19}{2\times 1}=190$
Total ways to select 2 students from 44 students:
${\hspace{0.17em}}^{44}{C}_2=\frac{44\times 43}{2\times 1}=946$
Required probability:
$P=\frac{190}{946}=\frac{95}{473}$

Therefore, the correct option is 95/473.