Question

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

Answer 1

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.