A bag has 3 red and k white marbles, where k > 1 is a positive integer. Two of the marbles are chosen at random from the bag. Given that the probability that the two marbles are of the same color is 1/2, find k.

Guest Jul 17, 2022

#1**0 **

The probability of getting 2 red marbles is \({3 \over 3 + k} \times {2 \over 2 + k} \)

The probability of getting 2 white marbles is \({k \over k + 3} \times { k - 1 \over k + 2}\)

This means that we have the equation \(\left(\frac{3}{3+k} \times \frac{2}{2+k}\right)+\left(\frac{k}{k + 3}\times \frac{k-1}{k+2}\right)=0.5\)

Now, just solve for k...

BuilderBoi Jul 17, 2022