Question

Margarita draws two cards from a standard deck of cards. Event A
is to draw any card from the suit of hearts without replacing it and event B
is to draw any red card. What is P(A∩B)
? Note that there are 26 red cards in a standard deck and that a suit includes 13 cards. Round your answer to the nearest tenths place.(1 point)
percent

Answer 1

To find \( P(A \cap B) \), we need to analyze the two events:

- Event \( A \): Drawing a heart.
- Event \( B \): Drawing a red card.

Since there are 13 hearts in a standard deck of cards, event \( A \) directly overlaps with event \( B \) since all hearts are red. Therefore, drawing a heart means that we have also drawn a red card.

When Margarita draws the first card, there are 52 cards in total. The outcomes for the events are as follows:

1. **Event A:** The first card drawn is a heart.
2. **Event B:** The first card drawn is a red card.

Now, since event \( A \) is part of event \( B \), \( P(A \cap B) \) is simply the probability of drawing a heart.

### Calculating \( P(A) \):

The probability of drawing a heart from the deck on the first draw is:

\[
P(A) = \frac{\text{Number of hearts}}{\text{Total number of cards}} = \frac{13}{52} = \frac{1}{4}
\]

### Conclusion

Since every heart drawn is also considered a red card, we can conclude that:

\[
P(A \cap B) = P(A) = \frac{1}{4}
\]

Now calculating the probability in percent:

\[
P(A \cap B) = \frac{1}{4} \times 100 = 25\%
\]

Therefore, the probability \( P(A \cap B) \) rounded to the nearest tenths place is:

\[
\boxed{25.0}
\]