Final answer:
The probability of drawing a heart or a queen from a standard deck of cards is 15 out of 52, as we need to count all the hearts and the remaining queens except the queen of hearts.
Step-by-step explanation:
The question asks for the probability of randomly selecting a heart or a queen from a standard deck of playing cards. In a standard deck, there are 13 hearts and 4 queens. However, since one of the queens is also a heart (the queen of hearts), there are 12 other hearts and 3 other queens (making a total of 16 possible cards) that meet the criteria without counting any card twice. Therefore, to find the probability, we add the probability of selecting a heart (13 out of 52) to the probability of selecting a queen from the other three suits (3 out of 52) and subtract the overlap which is the queen of hearts (1 out of 52)Probability = (Number of hearts + Number of queens from other suits - Queen of hearts) / Total number of cardsProbability = (13 + 3 - 1) / 5Probability = 15 / The probability of randomly selecting a heart or a queen can be calculated by adding the probabilities of selecting a heart and selecting a queen, then subtracting the
probability of selecting both a heart and a queen since they are not mutually exclusive events.There are 13 hearts in a deck of 52 cards, so the probability of selecting a heart is 13/52.There are 4 queens in a deck of 52 cards, so the probability of selecting a queen is 4/52Since there is 1 queen of hearts in a deck of 52 cards, the probability of selecting both a heart and a queen is 1/52To find the probability of selecting a heart or a queen, we can use the formulaP(heart or queen) = P(heart) + P(queen) - P(heart and queen)P(heart or queen) = (13/52) + (4/52) - (1/52Simplifying the expression gives:P(heart or queen) = 16/52The probability simplifies to 15 divided by 52, which can be reduced to approximately 0.2885 or 1 in 3.47, which is not represented by any of the provided options (a) 1/13, (b) 1/26, (c) 1/52, (d) 1/104. Hence, it seems there may have been a mistake in the question or the options provided.