Final answer:
To find the probability of randomly selecting specific cards from a standard deck, we count the favorable outcomes and divide by the total possible outcomes. The probability of selecting a club or a 3 is 4/13, the probability of selecting a red suit or a queen is 7/13, and the probability of selecting a 10 or a face card is 5/17.
Step-by-step explanation:
To find each probability, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
(1) The probability of randomly selecting a club or a 3 is the sum of the probabilities of selecting a club and selecting a 3, minus the probability of selecting a club that is also a 3.
There are 13 clubs and 4 threes in the deck, but one of the threes is also a club, so we subtract 1 from the total.
The probability is (13 + 4 - 1) / 52 = 16 / 52 = 4/13.
(2) The probability of randomly selecting a red suit or a queen is the sum of the probabilities of selecting a red suit and selecting a queen, minus the probability of selecting a red queen.
There are 26 red cards and 4 queens in the deck, but 2 of the queens are also red, so we subtract 2 from the total.
The probability is (26 + 4 - 2) / 52 = 28 / 52 = 7/13.
(3) The probability of randomly selecting a 10 or a face card is the sum of the probabilities of selecting a 10 and selecting a face card, minus the probability of selecting a 10 that is also a face card.
There are 4 tens and 12 face cards in the deck, but one of the tens is also a face card, so we subtract 1 from the total. The probability is (4 + 12 - 1) / 52 = 15 / 52 = 5/17.