A bag contains a number of pieces of candy of which 78 are red , 24 are brown , and the
remainder are yellow . If the probability of selecting a yellow piece of candy from this bag at
random is 1/3, how many yellow pieces of candy are in the bag?
Let's say the number of yellow pieces of candy in the bag is y.
The total number of candies in the bag is given by: 78 (red) + 24 (brown) + y (yellow).
The probability of selecting a yellow piece of candy at random is given by: number of yellow candies / total number of candies.
We are told this probability is 1/3, so we can set up the equation:
y / (78 + 24 + y) = 1/3
Simplifying the equation, we can multiply both sides by (78 + 24 + y):
y = (1/3)(78 + 24 + y)
Next, we can distribute the 1/3:
y = 26 + 8 + (1/3)y
Combining like terms, we get:
(2/3)y = 26 + 8
(2/3)y = 34
To isolate y, we can multiply both sides by 3/2:
y = (34)(3/2)
y = 51
Hence, there are 51 yellow pieces of candy in the bag.