Question

In a fair deck of cards, there are four aces and 26 red cards. If you draw one card from the deck, what is the probability that you will draw an ace or a red card?










53.8
57.8
55
51

Answer 1

To calculate the probability of drawing an ace or a red card from a standard deck of 52 cards, we can use the principle of addition for probabilities.

1. **Total number of cards**: There are 52 cards in a standard deck.
2. **Number of aces**: There are 4 aces in the deck.
3. **Number of red cards**: There are 26 red cards in the deck (which includes hearts and diamonds).
4. **Overlap**: Among the 4 aces, 2 of them (the ace of hearts and the ace of diamonds) are red cards.

Now we can calculate the number of favorable outcomes:

- The number of ways to draw an ace is 4.
- The number of ways to draw a red card is 26.
- Since 2 of the aces are included in the red cards, we need to subtract these to avoid double-counting:

\[
\text{Total favorable outcomes} = \text{Number of aces} + \text{Number of red cards} - \text{Number of overlapping aces}
\]

\[
= 4 + 26 - 2 = 28
\]

Now, we can find the probability:

\[
P(\text{Ace or Red Card}) = \frac{\text{Total favorable outcomes}}{\text{Total outcomes}} = \frac{28}{52} = \frac{7}{13}
\]

To convert this probability into a percentage, we can calculate:

\[
\frac{7}{13} \approx 0.5385
\]

Which is approximately \(53.85\%\).

Therefore, rounding to one decimal point, the probability that you will draw an ace or a red card is approximately:

**53.8%**.