Posted by Ian on .
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
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
it is the wrong answer
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.