The probability that a positive divisor of 60 is greater than 9 can be written as a/b, where a and b are coprime positive integers. What is the value of a+b?

To find the probability that a positive divisor of 60 is greater than 9, we first need to determine the total number of positive divisors of 60 and then count how many of them are greater than 9.

To find the total number of divisors of 60, we can factorize 60 into its prime factors. 60 can be written as 2^2 * 3 * 5. The total number of divisors can be obtained by multiplying each exponent of the prime factors by one more than that exponent and then taking the product.

For 2, we have (2^0, 2^1, 2^2) = (1, 2, 4) - three choices
For 3, we have (3^0, 3^1) = (1, 3) - two choices
For 5, we have (5^0, 5^1) = (1, 5) - two choices

Multiplying the number of choices for each prime factor, we get a total of 3 * 2 * 2 = 12 divisors for 60.

Next, we need to find how many of these divisors are greater than 9. The divisors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Among these, only 10, 12, 15, 20, 30, and 60 are greater than 9.

Therefore, the probability that a positive divisor of 60 is greater than 9 is 6/12 = 1/2.

Since 1 and 2 are coprime positive integers, the value of a+b is 1+2 = 3.