A card is drawn from a standard deck of 52 cards (four suits: clubs, hearts, diamonds, and spades; 13 values in each suit: ace, 2-10, jack, queen, and king). let event a be that the card drawn is a heart. let event b be that the card drawn is a face card (jack, queen, or king). what is the probability that a or b occurs? 25/52 22/52 16/52

P (A) = 13/52

P (B) = 12/52

It's important to know, firstly, that these events are not independent, as once event A has happened or not happened, the probability of B happening is altered;

In this case, we can find out what P (B|A) is by logic;

Let's say the card picked is of the suit hearts, this leaves 13 possible cards, which you could have picked, 3 of which are face cards;

So, the probability that the card you have picked is a face card is 3/13;

Thus, P (B|A) = 3/13;

Now, we can use this to find P (A∩B):

P (B|A) = P (A∩B) / P (A)

3/13 = P (A∩B) / (13/52)

P (A∩B) = 3/52

Next, we can use another formula to find P (A∪B):

P (A∪B) = P (A) + P (B) - P (A∩B)

P (A∪B) = 13/52 + 12/52 - 3/52

P (A∪B) = 22/52

Therefore, the answer is 22/52.

Note:

There is an alternative method, using P (A|B) instead of P (B|A) as I have done, but it yields the same answer.