In a cookie jar, there are 6 choco chip cookies and 8 oatmeal cookies. Kim takes out the cookies one at a time and proceeds to eat them. The probability that the 7th cookie that Kim eats is a choco chip cookie is a/b, where a and b are positive coprime integers. What is the value of a+b ?

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To find the probability that the 7th cookie Kim eats is a choco chip cookie, we need to determine the total number of cookies remaining after Kim eats the first 6 cookies.

Initially, there are 6 choco chip cookies and 8 oatmeal cookies, giving us a total of 6 + 8 = 14 cookies in the cookie jar.

To calculate the probability, we need the total number of possible outcomes and the number of favorable outcomes.

Since Kim is taking out the cookies one at a time, the total number of possible outcomes is the same as the number of cookies left in the jar after the first 6 cookies are eaten.

After Kim eats the first cookie, there are 14 - 1 = 13 cookies left.
After Kim eats the second cookie, there are 13 - 1 = 12 cookies left.
Continuing this pattern, after Kim eats the sixth cookie, there are 14 - 6 = 8 cookies left.

Now, let's consider the favorable outcome. We want the 7th cookie to be a choco chip cookie. After Kim eats the first 6 cookies (we don't know their type), the remaining choco chip cookies in the jar are 6 - 0 = 6.

Therefore, the probability that the 7th cookie Kim eats is a choco chip cookie is 6/8.

To find the value of a + b, we simply add a = 6 and b = 8, giving us a + b = 6 + 8 = 14.

Thus, the value of a + b is 14.