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Chapter 8: Problem 414

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

Identifying the number of favorable outcomes

There is only one ace of diamonds in the deck, so the number of favorable outcomes is 1.
02

Identifying the total number of outcomes

There are 52 cards in a standard deck of playing cards, so the total number of possible outcomes is 52.
03

Calculating the probability

Now that we have the number of favorable outcomes and the total number of outcomes, we can calculate the probability. To find probability, we simply need to divide the number of favorable outcomes by the total number of outcomes. Probability of drawing the ace of diamonds = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\) Probability of drawing the ace of diamonds = \(\frac{1}{52}\) Therefore, the probability of drawing the ace of diamonds from a thoroughly shuffled deck of playing cards is \(\frac{1}{52}\).

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