math probability question!!

Total number of cookies = 5 + 3 + 4 + 4 = 16

P(2 chocolate) = 5/16 X 4/15 = 1/12

P(2 peanut butter) = 3/16 X 2/15 = 1/40

P(2 oatmeal) = 4/16 X 3/15 = 1/20

P(2 sugar) = 4/16 X 3/15 = 1/20

As the above events are all mutually exclusive, so the required probability

= P(2 of the same kind)

= 1/12 + 1/40 + 1/20 + 1/20

= 5/24