SOLUTION: On a single draw from a shuffled standard deck of 52 cards, find the probability of obtaining (e). a three or a heart (f). a three and a heart

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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 which reduces to .

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 .

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