Within this probability exercise, what is a factor?

[syan]

This is part of a practice test for my upcoming TSI. I'm basically reviewing high school algebra concepts. I might overexplain things, but I'm trying to get all of my thoughts and questions down. The exercise in question reads:
2. Given the following set of numbers {1,1,1,1,2,3,4,5,5,5,5,6,7,8,8,8,8,8,9,10} what is the probability of choosing a prime number, given that a factor of 36 is chosen?

• A. 7/20
• B. 2/5
• C. 1/3
• D. 2/9

It's easy enough to determine that there are 11 chances out of the 20 that are prime: 11/20. However, this problem asks for the probability given a factor, being 36. I have no idea what a factor is, and in my frustration, got the question wrong. The answer was D: 2/9. I tried to reverse engineer the math, but to no avail. Can someone explain what a factor is in probability, and how it allows me to solve this problem?
To further elaborate on my understanding, I believe a factor to be a number that you can divide another number by, and get no remainder. I don't understand how my definition of factor can apply to this problem. I've googled "what is a factor in probability", as well as thought over how my understanding of a factor could apply to this problem.

 

[Harry_the_cat]

Yeah you have the definition of a factor correct. It is no different in probability questions.

Note that the factors of 36 listed here are 1,1,1,1, 2, 3, 4, 6, 9 ie 9 numbers. This becomes the denominator.

Out of those 9 numbers 2 and 3 are prime. ie 2 primes out of 9 factors of 36. This is the numerator.

So,
P(prime | factor of 36) = 2/9

(Note that | means "given that")

An alternative way is using the formula
$\displaystyle P(B|A) =\frac{P(A and B)}{P(A)}$
$\displaystyle =\frac{P(prime AND factor)}{P(factor)}$
$\displaystyle = \frac{2/20}{9/20}$
$\displaystyle =\frac{2}{9}$

 

[syan]

Yeah you have the definition of a factor correct. It is no different in probability questions.

Note that the factors of 36 listed here are 1,1,1,1, 2, 3, 4, 6, 9 ie 9 numbers. This becomes the denominator.

Out of those 9 numbers 2 and 3 are prime. ie 2 primes out of 9 factors of 36. This is the numerator.

So,
P(prime | factor of 36) = 2/9

(Note that | means "given that")

An alternative way is using the formula
$\displaystyle P(B|A) =\frac{P(A and B)}{P(A)}$
$\displaystyle =\frac{P(prime AND factor)}{P(factor)}$
$\displaystyle = \frac{2/20}{9/20}$
$\displaystyle =\frac{2}{9}$

Thanks, this makes perfect sense now. I'll mark this as solved.