Q. A bag contains 5 blue balls and unknown numbers of red balls, two balls are drawn at random. The probability of both of them are blue is $\frac{5}{14}$, then the number of red ballsare
A) 3
B) 2
C) 4
D) 5
Explanation
(a)
Let the number of red balls be $x$.
According to the given condition,
$\frac{\ ^{5}C_{2}}{\ ^{5 + x}C_{2}} = \frac{5}{14}$
$\Rightarrow \ \frac{20(3 + x)!}{(5 + x)!} = \frac{5}{14}$
$\Rightarrow \ 56 = (5 + x)(4 + x)\ \Rightarrow \ x = 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.