vinoo7 wrote:
In a bag there are a certain number of black balls and white balls. The probability of picking up exactly 1 white ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of black balls to white balls in the bag
A. 1:7
B. 2:1
C. 1:1
D. 4:1
E. 1:4
Hi, I did it with another method, it took a lot of trial and error to find a way to solve this one. At first I took the pure algebraic way to solve it, but no joy. Then I kind of tweaked my method a bit. I have taken a method similar to
chetan2u. As we have been asked the ratio of Black and White balls, let's call the ratio k.
Let the number of Black balls = kx
Let the number of White balls = x
Now let's write the probability expression
\(\frac{(Number of ways of selecting one white ball*Number of ways of selecting one black ball)}{Total number of ways of selecting any two balls}\)
\(\frac{(kx*x)}{(kx + x)(kx + x - 1)} = \frac{1}{2}\)
on simplifying we get
\(x^2(k^2 + 1 - 2k) = x(k + 1)\)
Here, we know that x(number of white balls) is positive and an integer. So we can simply cut x here
\(x(k^2 + 1 - 2k) = (k + 1)\)
\(x = \frac{(k + 1)}{(k^2 + 1 - 2k)}\)
Now, we know that x has to be an integer. From here, we can try values for k from options such that x turns out to be an integer.
Only (B) satisfies.
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