Pre Calc Probability Word Problem

Question

there are 5 red balls, 30 black balls, and 7 pink balls in a jar. You pull one out, don't replace it, and pull another one out. Find the probability of getting two of the same color?

Please include work! Thank You!

Answer 1

5, 30 and 7 of different colors

total 42

5/42 times 4/41 for one way to get the same color

30/42 times 29/41 for another way

7/42 times 6/41 is a 3rd way

add them up to get the probability of having 2 of the same color on 2 draws without replacement

= (5/42)(4/41) + (30/42)(29/41) + (7/42)(6/41)

= (20 + 870 + 42)/(41)(42) = 932/1722 = about 54%