Question

In a cookie jar there are 9 sugar cookies and 12 snickerdoodle cookies. The cookie are randomly mixed together in the jar. What is the probability of pulling two of the same types of cookies out of the cookie jar in a row without replacement?

Answer 1

The probability of pulling two of the same types of cookies in a row without replacement is
`(51)/(105)`.

Explanation:

There are a total of 21 * 20 = 420 different outcomes (After you take one cookie out, you aren't replacing it, so there will be 20 cookies in the jar on the second grab). There are a total of 9 * 8 = 72 different combinations of two sugar cookies, and 12 * 11 = 132 different combinations of two snickerdoodle cookies, so the total probability of pulling two of the same types of cookies in a row without replacement is
`(132+72)/(420) = (204)/(420) = (51)/(105)`.