A box contains colored balls: red, green, blue, and yellow. If the box contains 12 green balls, where the probability of drawing one of them randomly is one-sixth, what is the total number of balls in the box?
First of all, we wanna think about what probability is. It’s the desired outcome over all possible outcomes. And for us, that selected outcome will be choosing a green ball out of the total number of all the balls. And we’ve been told that this probability is one-sixth. But we’ve also been told that there are 12 green balls. And we need to take that and find out what the total number of balls in the box are. This probability of one-sixth has been simplified. It’s been reduced. And we know the total numbers will be proportional to the probability.
To get from one to 12, we multiply the numerator by 12. And since these values are proportional, if we multiply by 12 in the numerator, we need to multiply by 12 in the denominator. And six times 12 is 72. What we see is that 12 over 72 simplifies to one-sixth, and so the probability of selecting green is one-sixth. But since there are 12 green balls, there are 72 total balls.