Question

A box contains cards number 1-10. A card is drawn at random, then replaced, and a second card is drawn. What is the probability that the first number is a multiple of 5 and the second number is prime?

Answer 1

You would solve this by determining how many numbers from 1-10 can be multiples of 5.  That's obviously 5 and 10.  So that's 2/10 or reduced to 1/5.  Now the second question you have to find how many numbers from 1-10 are prime.  Prime is a number that can only be divided by 1 and itself.  So that would leave you with 1, 3, 5, 7.  I think where the trick comes into play is if you drew a 5 or 10 the first time, then you didn't place those cards back in the box, you couldn't draw them again.  So the answer would 4/10 or 2/5 if you could draw the 5 again.  Or I supposed if you had drew the 10 the first time and not the 5.  I assume however, they want you to exclude 5 and 10 because it was part of the first section of this equation.  So that would mean only 1, 3, and 7 or 3/10.