In order to make the probability of selecting a black marble 1/5, how many black marbles should be added to the jar?

Question

A jar contains 23 marbles, 3 marbles are black and the rest are red. 

Answer 1

Originally there are 3 black marbles and 20 red marbles 

 

The probability of selecting a black marble is equal to the number of black marbles divided by the total number of marbles.    

 

If X black marbles are added to the jar there will be 3 + X black marbles and (3 + X + 20) total marbles 

 

To have the probability of selecting a black marble be 1/5 the ratio of black marbles to total marbles must be 1/5  ==> 

 

(3+X)/(3+X+20) = 1/5

23 + X = 15 + 5X

8 = 4X

X = 2 black marbles should be added to the jar 

 

Check: After 2 black marbles are added there will be 5 black marbles and 25 total marbles so 

           P(Black) = 5/25 = 1/5