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Chapter 2: Problem 88

A deck of playing cards is thoroughly shuffled and a card is drawn from the deck. What is the probability that the card drawn is the ace of diamonds?

Short Answer

Expert verified
The probability of drawing the Ace of Diamonds from a thoroughly shuffled deck of playing cards is \(\frac{1}{52}\).

Step by step solution

01

Identify the total number of outcomes

In a standard deck of playing cards, there are 52 cards in total. This means that there are 52 possible outcomes when drawing a single card from the deck.
02

Identify the favorable outcomes

The Ace of Diamonds is a unique card and there is only one amongst the 52 cards in the deck. In this case, the favorable outcome is drawing the Ace of Diamonds. Therefore, there is only 1 favorable outcome.
03

Calculate the probability

To calculate the probability of an event, we can use the formula: Probability = (Number of favorable outcomes) / (Total number of outcomes) Plugging in the numbers from Steps 1 and 2, we get: Probability = \(\frac{1}{52}\)
04

Simplify the probability (if necessary)

In this case, the probability \(\frac{1}{52}\) is already in its simplest form, so no further simplification is needed.
05

Write the result

The probability of drawing the Ace of Diamonds from a thoroughly shuffled deck of playing cards is \(\frac{1}{52}\).

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