I think there's an easy way and a hard way to do this, and I think that the way
I'm about to describe is the easier way.
Probability = (number of successful outcomes)/(total number of possible outcomes)
How many total pairs can be drawn from 8 total pens ?
-- The first one drawn can be any one of 8 pens. For each of these . . .
-- The second one drawn can be any one of the remaining 7 .
-- Total number of ways of drawing a pair = (8 x 7) = 56 ways.
-- But there aren't 56 different different pairs. Whether you draw A and then B,
or B and then A, you wind up with the same pair. There are 2 different ways to
draw each pair, so the 56 ways of drawing a pair only produces 28 different pairs.
How many pairs are two of the same color ?
Possible number of blue pairs:
The reasoning is exactly the same as calculating the TOTAL number of
pairs, as explained above.
With 5 blue pens, you can make 10 different pairs.
AB, AC, AD, AE, BC, BD, BE, CD, CE, and DE.
Possible number of red pairs:
The reasoning is exactly the same as calculating the TOTAL number of
pairs, as explained above.
With 3 red pens, you can make 3 different pairs.
AB, AC, and BC.
Total number of possible same-color pairs = 10 + 3 = 13
successes / total possible outcomes = 13/28 = 46.4% (rounded)
