# Maths

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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 ab, 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

• Maths -

could be RR, GG, YY, or BB
prob RR = (10/40)(9/39) = 3/52

the others are the same calculation
so prob = 4(3/52) = 9/52

now doing the a and b stuff
a=9 , b=52
a+b = 61

• Maths -

• Maths -

The first one can be any color. But after you draw it there will be only 9 of that color left.

So the odds of drawing the same color again are 9/39.

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