Question 128018
On a single draw from a deck of 52 cards, exactly 52 different things could happen.  For part e, you will consider yourself successful if you get a three or a heart.  There are 4 cards with the value three, and 13 hearts, but one of those hearts is also one of the threes, so there are 16 ways you can have a success, the 3 threes that aren't hearts, and the 13 hearts (You could also count it as the 4 threes and the 12 hearts that aren't a three, but you still get to 16).


So if you have 16 ways you can be successful out of 52 ways something could happen, the probability is {{{16/52}}} which reduces to {{{4/13}}}.


For part f, you want a three and a heart.  In other words, you want the three of hearts.  There is only one of these in the deck, so you only have one of the 52 possibilities that you can consider a success and your probability is {{{1/52}}}.


I am very good at card probability problems -- a sure sign of a mis-spent youth.