Calculate the probability of drawing an ace 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 52 cards in total, which include 4 aces (one from each suit: hearts, diamonds, clubs, and spades). To find the probability of drawing one of these aces, you need to determine the ratio of the number of successful outcomes (drawing an ace) to the total number of possible outcomes (drawing any card from the deck).

Here, the number of successful outcomes is 4 (the four aces), and the total number of possible outcomes is 52 (the total cards in the deck). The probability is calculated as:

[

\text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{52}

]

This fraction can be simplified. Dividing both the numerator and the denominator by 4 gives:

[

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

]

Thus, the probability of drawing an ace from a standard deck of cards is ( \frac{1}{13} ). This choice accurately represents the calculated probability based on the total number of aces and the overall card count in the deck.

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