Marbles

Probability Level 2

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?

2 10 5 8 3

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Prathamesh Samal by Prathamesh Samal , 19, India

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2 solutions

Yasir Soltani
Feb 4, 2016

Let n n be the number of Red Marbles \textbf{Red Marbles} then the number of Blue Marbles \textbf{Blue Marbles} is 4 n 4n by the second condition we have

n + 5 ( n + 5 ) + 4 n = 1 3 \frac{n+5}{(n+5)+4n}=\frac{1}{3} 3 n + 15 = 5 n + 5 3n+15=5n+5 2 n = 10 2n=10 n = 5 \boxed{n=5}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Brilliant solution Yasir Soltani

Prathamesh Samal - 5 years, 4 months ago
Roger Erisman
Jan 29, 2016

r/{r+b} = 1/5

5r = r + b

4r = b Eqn. 1

{r +5}/{r +5+b} = 1/3

3r + 15 = r + 5 + b

2r + 10 = b Eqn. 2

Combining 1 and 2

4r = 2r + 10

2r = 10

r = 5

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice solution

Prathamesh Samal - 5 years, 4 months ago

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