Question Details

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.

Options

37/247

95/473

33/473

25/214

Show Answer

Correct Answer :

Option B

95/473

Solution :

From the given scatter chart, we can determine the number of boys (represented on the Y-axis) and the number of girls (represented on the X-axis) for classes P, Q, and R:
- Class P: Boys = 40, Girls = a + b
- Class Q: Boys = 20, Girls = a + 3b
- Class R: Boys = 60, Girls = a + 5b

Step 1: Find the number of girls in Class R
Let the number of girls in class R be $G_{R} = a + 5 b$ .
According to the given condition, if there were 10 more girls in class R, the probability of selecting a girl from class R would be 40%.
The new number of girls in class R would be $G_{R} + 10$ , and the total number of students in class R would be:
$Total students in R = G_{R} + 10 + 60 = G_{R} + 70$
Setting up the probability equation:
$\frac{G_{R} + 10}{G_{R} + 70} = \frac{40}{100} = \frac{2}{5}$
Cross-multiplying to solve for $G_{R}$ :
$5 (G_{R} + 10) = 2 (G_{R} + 70)$
$5 G_{R} + 50 = 2 G_{R} + 140$
$3 G_{R} = 90$
$G_{R} = 30$
Therefore, the number of girls in class R is 30.

Step 2: Find the number of girls and boys in Class Q
We are given that the number of girls in class Q is $\frac{200}{3} %$ the number of girls in class R:
$G_{Q} = \frac{200}{3} \times \frac{1}{100} \times 30 = \frac{2}{3} \times 30 = 20$
From the scatter chart, the number of boys in class Q is:
$B_{Q} = 20$

Step 3: Calculate the number of boys and girls in Class S
For class S, the number of girls is the same as that of class Q:
$G_{S} = G_{Q} = 20$
The number of boys in class S is 20% more than the boys in class Q:
$B_{S} = 20 + (20 % of 20) = 20 + 4 = 24$
So, the total number of students in class S is:
$Total students = 20 + 24 = 44$

Step 4: Find the probability of selecting two girls from Class S
The number of ways to select 2 girls out of 20 is given by combinations:
$^{20} C_{2} = \frac{20 \times 19}{2} = 190$
The total number of ways to select any 2 students out of 44 is:
$^{44} C_{2} = \frac{44 \times 43}{2} = 946$
The probability of selecting two girls is:
$Probability = \frac{190}{946} = \frac{95}{473}$