From a bag containing 12 identical blue balls, y identical yellow balls,and no other balls,one ball will be removed at random.If the probability is less than 2/5 that the removed ball will be blue,what is the least number of yellow balls that must be in the bag?

a)17
b)18
c)19
d)20
e)21



"The probability is less than 2/5 that the removed ball will be blue."
It can be written as: P(B is out)<2/5

You have 12 blue balls and y yellow balls. The total of balls is: 12+y
So you can write P(B is out)=12/(12+y)

Now you want to find the number of y yellow balls required to get the inequality true, so you join both lines we wrote, it gives you:
12/(12+y)<2/5
60<24+2y
36<2y
18<y

So if we want to have the inequality "P(B i out)" true we need at least 19 for y