a is chosen from the set {1,2,3,4}, and b is chosen from the set {5,6,7,8,9,10}. What is the probability that the product ab is a prime number?

You have a total of: 4 x 6 ==24 products

Since a prime is only divisible by 1 and itself, it therefore follows that can you only have:

1 x 5 ==5 and 1 x 7==7

Therefore, the probability is: 2 / 24 ==1 / 12