Abag 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?

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

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