A box contains 5 red and k blue balls. A ball is selected at random from the box. If the probability of selecting a blue ball is \(\frac{2}{3}\), find the v...

A box contains 5 red and k blue balls. A ball is selected at random from the box. If the probability of selecting a blue ball is \(\frac{2}{3}\), find the value of k.

Answer Details

Let's first calculate the total number of balls in the box. The box contains 5 red balls and k blue balls, so the total number of balls is 5 + k. The probability of selecting a blue ball can be calculated as follows: P(blue ball) = (number of blue balls) / (total number of balls) We are told that this probability is \(\frac{2}{3}\), so we can set up the following equation: \(\frac{k}{5+k} = \frac{2}{3}\) Cross-multiplying and simplifying, we get: 3k = 10 + 2k k = 10 Therefore, there are 10 blue balls in the box. Answer: 10.