Final answer:
The probability of drawing a queen or a heart from a deck of 52 cards is found using the Addition Rule, which accounts for the overlap of the queen of hearts. It is calculated as 16/52, or approximately 30.77%.
Step-by-step explanation:
To calculate the probability of drawing a queen or a heart from a well-shuffled deck of 52 cards using the Addition Rule, we start by establishing the individual probabilities. There are 4 queens in the deck, one in each suit, and 13 hearts.
The probability of drawing a queen is 4 out of 52, or 4/52. The probability of drawing a heart is 13 out of 52, or 13/52. However, since one of the queens is also a heart (the queen of hearts), we must adjust for this overlap. The Addition Rule for probabilities states that the probability of either event occurring is the sum of the probabilities of each event, minus the probability of both events occurring together.
So, to use the Addition Rule:
- Probability of a queen: P(Q) = 4/52
- Probability of a heart: P(H) = 13/52
- Probability of a queen of hearts (overlap): P(Q and H) = 1/52
We apply the Addition Rule:
P(Q or H) = P(Q) + P(H) - P(Q and H)
P(Q or H) = (4/52) + (13/52) - (1/52)
P(Q or H) = 16/52 or approximately 0.3077
Therefore, the probability of drawing either a queen or a heart from a deck of 52 cards is 16/52, or about 30.77%.