Marbles Without Replacement

Probability Level 3

A bag contains $10$ red marbles, $10$ green marbles, $10$ yellow marbles and $10$ blue marbles. You reach into the bag and grab a marble, then reach into the bag and grab a second marble. The probability that the second marble is the same color as the first marble is $\frac{a}{b}$ , where $a$ and $b$ are positive, coprime integers. What is the value of $a+b$ ?

Note: You do not place the first marble back into the bag.

The answer is 16.

1 solution

Arron Kau Staff
May 13, 2014

The first marble can be any color - red, green, yellow or blue. If the second marble is the same color, then there are only $9$ remaining marbles of that color with $39$ total marbles remaining in the bag. Thus the probability is $\frac{9}{39} =\frac{3}{13}$ .

Hence $a+b =3+13 = 16$ .

Marbles Without Replacement

The answer is 16.

1 solution

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