What is the probability of drawing a heart from a standard deck of cards?

Study for the HSC Mathematics Standard 2 Exam. Utilize flashcards and multiple choice questions, each with hints and explanations. Prepare confidently for your exam success!

In a standard deck of cards, there are a total of 52 cards, which consist of 4 suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards. When considering the probability of drawing a heart, you focus solely on the number of hearts in the deck. There are 13 hearts out of 52 total cards.

To find the probability of drawing a heart, you use the ratio of the number of hearts to the total number of cards. This calculation is as follows:

[

\text{Probability of drawing a heart} = \frac{\text{Number of hearts}}{\text{Total number of cards}} = \frac{13}{52}

]

Simplifying this fraction gives:

[

\frac{13}{52} = \frac{1}{4}

]

Therefore, the probability of drawing a heart from a standard deck of cards is indeed 1/4. This approach to calculating probability helps clarify why the answer given aligns with the fundamental concepts of probability regarding equally likely outcomes within a defined sample space.

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