Question

A card is drawn from a deck of 52 playing cards. What is the probability that it is a king (4 king cards in a deck) or a red card (26 red cards in a deck)? Reduce the fraction. (1 point) Responses 513 5 over 13 713 7 over 13 413 4 over 13 313

Answer 1

To find the probability of drawing either a king or a red card from a standard deck of 52 playing cards, we can use the principle of inclusion-exclusion.

1. **Total number of cards**: 52
2. **Number of kings**: 4 (the kings of hearts, diamonds, clubs, and spades)
3. **Number of red cards**: 26 (13 hearts and 13 diamonds)
4. **Kings that are red**: 2 (the king of hearts and the king of diamonds)

Now we apply the formula:

\[
P(\text{King or Red}) = P(\text{King}) + P(\text{Red}) - P(\text{King and Red})
\]

Calculating each probability:

- \( P(\text{King}) = \frac{4}{52} \)
- \( P(\text{Red}) = \frac{26}{52} \)
- \( P(\text{King and Red}) = \frac{2}{52} \)

Now substituting into the inclusion-exclusion formula:

\[
P(\text{King or Red}) = \frac{4}{52} + \frac{26}{52} - \frac{2}{52} = \frac{4 + 26 - 2}{52} = \frac{28}{52}
\]

Next, we simplify \( \frac{28}{52} \):

\[
\frac{28 \div 4}{52 \div 4} = \frac{7}{13}
\]

So, the probability that the card drawn is either a king or a red card is \( \frac{7}{13} \).

Thus, the correct response is:

**7 over 13**.