Final answer:
Calculating the probabilities of different outcomes when drawing from a standard deck of 52 cards involves understanding the composition of the deck and applying combinatoric principles. Probabilities of specific combinations, such as drawing a black Queen, or drawing a card that is black and a face card, require counting the relevant cards and dividing by the total number of cards in the deck.
Step-by-step explanation:
The question asks about several probabilities related to drawing cards from a standard deck of 52 cards. We can calculate each individual probability based on the composition of the deck. Here are the probabilities explained:
- P(black and a Queen): There are two black queens in a deck (one in spades and one in clubs), so the probability of drawing a black queen is 2/52.
- P(black or a 3): Since there are two black suits (clubs and spades), there are 26 black cards, plus there are four '3's in a deck. However, two of the '3's are black, and we must avoid counting them twice. Therefore, the total is 26 black cards + 2 non-black '3's, which equals 28, so the probability is 28/52.
- P(face card or a number card): All cards in a deck are either face cards or number cards. There are 12 face cards (3 in each suit), and the rest are number cards. Since this accounts for the entire deck, the probability is 52/52 or 1.
- P(black and a face card): There are 3 face cards in each of the two black suits, which makes 6 black face cards. Thus, the probability is 6/52.
- P(Queen and a 3): The probability of drawing a card that is both a queen and a 3 is impossible since no card can be both. Hence, the probability is 0.
These probabilities represent basic Card Probability problems in Combinatorics, a field of Mathematics that deals with counting, both as an abstract concept and in terms of calculating the likelihood of events.