Statistics and Probability

Question

There are 10 red, 5 blue and 3 green shirts in a drawer. A shirt is selected and  returned to the drawer and then the second shirt is selected. What is the probability that the shirts are of different color?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

Answer 1

There are three ways that you could draw the same shirt twice. You could draw a red shirt twice, a blue shirt twice, or a green shirt twice. We will compute the probability of each case, and then add them up.

Case 1: Red shirt drawn twice. The probability of drawing the red shirt the first time is 10/20, and the probability of drawing the red shirt the second time is 10/20. So the probability of drawing the red shirt twice is 10/20*10/20 = 1/2*1/2 = 1/4

Case 2: Blue shirt drawn twice. The probability of drawing the blue shirt the first time is 5/20, and the probability of drawing the blue shirt the second time is 5/20. So the probability of drawing the blue shirt twice is 5/20*5/20 = 1/4*1/4 = 1/16

Case 3: Green shirt drawn twice. The probability of drawing the green shirt the first time is 3/20, and the probability of drawing the green shirt the second time is 3/20. So the probability of drawing the green shirt twice is 3/20*3/20 = 9/400

So the total probability is 1/4+1/16+9/400 = 0.335 = 335/1000 = 67/200