A bag has a number of identical balls; 78 balls of them are green, and the rest are blue. Given that the probability of drawing a blue ball is , determine the number of the blue balls.
Let be the event "green is selected" and be the event "blue is selected".
There are only blue balls and green balls in the bag so
and are complementary events and their probabilities add up to 1.
We know that .
If there are identical balls in the bag, the probability that a green ball is
selected is given by
We know there are 78 green balls and that .
So the number of blue balls in the bag is