Question

A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag?

Answer 1

If there are x red marbles initially then 1/5 is a probability in it's lowest form cancelled down from:

1/5 = x/5x

so there are 5x total marbles, x red and 4x blue.
Add 5 new red and the new probability is:

(x+5)/(5x+5) = 1/3

3x+15 = 5x+5

2x = 10

originally there were:

x = 5 red
4x = 20 blue

marbles.

***************
there are now:

x+5 = 10 red
4x = 20 blue

marbles

Answer 2

1 because their are only 1 in 5 chance to get a red one