To find the probability of not drawing a heart from a standard deck of 52 cards, we can follow these steps:
1. Identify the total number of cards in the deck.
- A standard deck of cards has a total of 52 cards.
2. Identify the number of heart cards in the deck.
- In a standard deck, there are 13 hearts (since each of the four suits - hearts, diamonds, clubs, and spades - contains 13 cards).
3. Calculate the number of non-heart cards in the deck.
- Since there are 52 cards in total and 13 of those are hearts, the number of non-heart cards can be calculated as:
[tex]\[
\text{Number of non-heart cards} = \text{Total cards} - \text{Number of hearts} = 52 - 13 = 39
\][/tex]
4. Determine the probability of drawing a non-heart card.
- The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case:
[tex]\[
P(\text{not heart}) = \frac{\text{Number of non-heart cards}}{\text{Total number of cards}} = \frac{39}{52}
\][/tex]
5. Express the result in the desired form.
- To express the probability as a decimal:
[tex]\[
\frac{39}{52} \approx 0.75
\][/tex]
Therefore, the probability of not drawing a heart from a standard 52 card deck is 0.75. In fraction form, it is [tex]\(\frac{39}{52}\)[/tex], which can be simplified further if needed. In this case, the simplest fraction form is already [tex]\(\frac{39}{52}\)[/tex].
