Final answer:
The probability of drawing a queen from a standard 52-card deck is about 0.077. The probability of drawing either a face card or a black card is approximately 0.615.
Step-by-step explanation:
The probability of drawing a queen from a standard 52-card deck is calculated by dividing the number of queens in the deck by the total number of cards in the deck. Since there are four queens and 52 cards total, the probability is:
1) P(queen) = Number of queens / Total number of cards
= 4 / 52
= 1 / 13
≈ 0.076923 (rounded to three decimal places)
For the probability of drawing either a face card or a black card, we first identify the total number of face cards, which is 12 (three in each suit), and the number of black cards, which is 26 (13 clubs + 13 spades). However, some face cards are also black (there are 6 black face cards), and we don't want to double-count these.
So, we add the number of face cards to the number of black cards and subtract the number of black face cards. The probability is:
2) P(face or black) = (Number of face cards + Number of black cards - Number of black face cards) / Total number of cards = (12 + 26 - 6) / 52
= 32 / 52
= 8 / 13
≈ 0.615384 (rounded to three decimal places)