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marbles

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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.

Jul 17, 2022

#1
+2448
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...

Jul 17, 2022
#2
+1

Thanks for the help!

Guest Jul 17, 2022