If Yasin has five red balls and two white balls, then the probability of picking a red ball is 5/7 and the probability of picking a white ball is 2/7. To make it just as likely that he will pick a red ball as a white ball, the probability of picking a red ball or a white ball must be 1/2.
Let x be the number of white balls Yasin needs to add to the bag. Then, the total number of balls in the bag will be 5 + x red balls and 2 + x white balls.
The probability of picking a red ball will be (5)/(7 + x) and the probability of picking a white ball will be (2 + x)/(7 + x).
We can set up an equation:
5 / (7 + x) = (2 + x) / (7 + x)
Solving for x, we get:
5(7 + x) = (2 + x)(7 + x)
35 + 5x = 14 + 9x + x^2
x^2 + 4x - 21 = 0
(x + 7)(x - 3) = 0
The solution x = 3 makes sense since if Yasin adds 3 more white balls, then the bag will have 5 red balls and 5 white balls, making it equally likely to pick a red ball or a white ball.