For each of the following determine the probability. A card is drawn from a standard deck of 52 cards. Enter your answers as reduced fractions or exact decimals. What is the probability that it is: a) a Queen OR a 4 ? Enter your answer b) a black 6 OR a red 4 ? Enter your answer a 2 OR a black card? Enter your answer d) an even-numbered card OR a black card? Enter your answer e) a Heart OR a 10? Enter your answer

To calculate the probabilities, we first recognize the total number of cards in a standard deck is 52. Let’s break down the individual probabilities for each part: a) The probability of drawing a Queen OR a 4: There are 4 Queens and 4 Fours in the deck, but since they are different cards, we can simply add their probabilities. Probability = (4 Queens + 4 Fours) / 52 = 8/52 = 2/13. b) The probability of drawing a black 6 OR a red 4: There are 2 black 6's (6 of Spades and 6 of Clubs) and 2 red 4's (4 of Hearts and 4 of Diamonds). Probability = (2 black 6's + 2 red 4's) / 52 = 4/52 = 1/13. c) The probability of drawing a 2 OR a black card: There is 1 two (2 of Hearts) and 26 black cards (Spades and Clubs combined). Because the 2 of Hearts is not black, we can add these two probabilities directly. Probability = (1 two + 26 black cards) / 52 = 27/52 = 27/52. d) The probability of drawing an even-numbered card OR a black card: Even-numbered cards consist of 2, 4, 6, 8, and 10, totaling 20 (10 cards from Hearts/Diamonds and 10 from Spades/Clubs). Since 26 cards are black (which includes even-numbered ones), we must be careful not to double-count. There are 10 even black cards. Probability = (20 even cards + 26 black cards - 10 even black cards) / 52 = 36/52 = 9/13. e) The probability of drawing a Heart OR a 10: There are 13 Hearts in a deck and 4 tens (10 of Hearts included already). We need to account for this overlap. Probability = (13 Hearts + 4 tens - 1 overlapping card) / 52 = 16/52 = 4/13. Here are the final answers: a) 2/13 b) 1/13 c) 27/52 d) 9/13 e) 4/13