Question

In a fair deck of cards, what is the probability of drawing a black four or a heart?









28.8
53.8
32.7
23.6

Answer 1

To determine the probability of drawing a black four or a heart from a standard deck of 52 playing cards, we need to calculate the total number of favorable outcomes and then divide that by the total number of outcomes (which is 52).

1. **Count the black fours:** There are 2 black fours in the deck (the four of clubs and the four of spades).

2. **Count the hearts:** There are 13 hearts in the deck.

3. **Check for overlap:** The black fours are not hearts, so there is no overlap between the two groups we're interested in.

Now we can apply the principle of inclusion-exclusion to find the total number of favorable outcomes:

\[
\text{Total favorable outcomes} = (\text{Number of black fours}) + (\text{Number of hearts}) - (\text{Number of overlaps})
\]
\[
= 2 + 13 - 0 = 15
\]

The probability \( P \) of drawing a black four or a heart is then:

\[
P = \frac{\text{Total favorable outcomes}}{\text{Total outcomes}} = \frac{15}{52}
\]

To convert this to a percentage:

\[
P \approx \frac{15}{52} \times 100 \approx 28.8\%
\]

Thus, the probability of drawing a black four or a heart is approximately **28.8%**. Therefore, the answer is:

**28.8**