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 it and get 98 points if you get it right

Answer 1

Let red marbles = X.

The probability is 1 out of 5, written as 1/5

1/5 in terms of red marbles is equal to the number of red marbles divided by 5x, where 5x is the total number of marbles.

1/5 = x/5x

Now you have 5x total marbles, x red and 4x blue.

Add 5 more red and the new probability is:

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

Simplify:

3x+15 = 5x+5

Now solve for x:

Subtract 3x from both sides:

15 = 2x +5

Subtract 5 from each side:

2x = 10

Divide both sides by 2:

x = 10/2

X = 5

There were originally 5 red marbles.