In a cookie jar, there are 6 chocolate cookies and 8 oatmeal cookies. I take out the cookies one at a time and proceed to eat them. The probability that the 7th cookie that I eat is a chocolate cookie is a/b, where a and b are positive coprime integers. What is the value of a+b?

10 (3/7)

To find the probability that the 7th cookie you eat is a chocolate cookie, we need to determine the total number of cookies left in the jar after eating the first six cookies.

Initially, there are 6 chocolate cookies and 8 oatmeal cookies, making a total of 14 cookies in the jar. If you eat one cookie at a time, the number of cookies left in the jar decreases by 1 after each cookie you eat.

After eating the first chocolate cookie, there are 5 chocolate cookies and 8 oatmeal cookies left in the jar, totaling 13 cookies. Similarly, after eating the second chocolate cookie, there are 4 chocolate cookies and 8 oatmeal cookies left (12 in total). This pattern continues until you eat the 6th chocolate cookie. At that point, there will be only 1 chocolate cookie remaining in the jar, along with the 8 oatmeal cookies, resulting in a total of 9 cookies.

Therefore, the probability of the 7th cookie being chocolate is 1 out of 9, or 1/9. So a = 1 and b = 9.

To find the value of a+b, simply add the values of a and b: 1 + 9 = 10.

Therefore, the value of a+b is 10.