There are 4 suits (heart, diamond, clover and spade) in a 52 -card deck, and each suit has 13 cards. Suppose an experiment is to draw one card from a deck and observe what suit it is.
    Enter answer as a reduced fraction or a decimal rounded to 2 decimal places.
a         What is the probability of drawing a heart or diamond?
b         What is the probability of drawing a king or a red card?
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The Correct Answer and Explanation is :
a. What is the probability of drawing a heart or diamond?
There are 13 hearts and 13 diamonds in a 52-card deck. P(heart or diamond)=13+1352=2652=12=0.50\text{P(heart or diamond)} = \frac{13 + 13}{52} = \frac{26}{52} = \frac{1}{2} = 0.50P(heart or diamond)=5213+13=5226=21=0.50
Answer: 1/2 or 0.50
b. What is the probability of drawing a king or a red card?
- There are 4 kings in total (1 per suit).
- There are 26 red cards (13 hearts + 13 diamonds).
- However, 2 kings are red (king of hearts and king of diamonds).
To avoid double-counting, use the formula for union of two events: P(King or Red)=P(King)+P(Red)−P(King AND Red)\text{P(King or Red)} = \text{P(King)} + \text{P(Red)} – \text{P(King AND Red)}P(King or Red)=P(King)+P(Red)−P(King AND Red) =452+2652−252=2852=713≈0.54= \frac{4}{52} + \frac{26}{52} – \frac{2}{52} = \frac{28}{52} = \frac{7}{13} \approx 0.54=524+5226−522=5228=137≈0.54
Answer: 7/13 or 0.54
Explanation (300+ words)
In probability theory, when we are interested in the likelihood of one or more events occurring, it is important to understand whether the events overlap. This is especially crucial when calculating the probability of compound events like “drawing a heart or a diamond” or “drawing a king or a red card.”
Part (a): Heart or Diamond
A standard 52-card deck contains 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards. Hearts and diamonds are both red suits. Since they don’t overlap (a single card cannot be both a heart and a diamond), we simply add their probabilities: 1352+1352=2652=12\frac{13}{52} + \frac{13}{52} = \frac{26}{52} = \frac{1}{2}5213+5213=5226=21
This means there is a 50% chance of drawing a heart or diamond when one card is drawn.
Part (b): King or Red Card
Now, the probability of drawing either a king or a red card is slightly more complex. There are 4 kings and 26 red cards. However, two of the kings are red. If we just add the probabilities: 452+2652=3052\frac{4}{52} + \frac{26}{52} = \frac{30}{52}524+5226=5230
This overcounts the two red kings. So, we subtract the overlap: 30−252=2852=713\frac{30 – 2}{52} = \frac{28}{52} = \frac{7}{13}5230−2=5228=137
This tells us there’s a roughly 53.85% chance of drawing either a king or a red card. Understanding overlaps prevents errors in compound probability and is key to mastering basic statistics.