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Chapter 2: Problem 90

Find the probability of drawing a black card in a single random draw from a well-shuffled deck of ordinary playing cards.

Short Answer

Expert verified
The probability of drawing a black card in a single random draw from a well-shuffled deck of ordinary playing cards is \(\frac{1}{2}\) or 50%.

Step by step solution

01

Identify the number of favorable outcomes

In a standard deck of playing cards, there are 13 Spades (black) and 13 Clubs (black). So, there are 26 black cards.
02

Identify the total number of possible outcomes

A standard deck of playing cards has 52 cards in total, making 52 the total number of possible outcomes in this case.
03

Calculate the probability

Now, apply the probability formula: Probability (P) = (Number of favorable outcomes) / (Total number of possible outcomes) P (drawing a black card) = \(\frac{26}{52}\)
04

Simplify the fraction

Simplify the fraction (if possible) to get the final probability: P (drawing a black card) = \(\frac{26}{52} = \frac{1}{2}\) Hence, the probability of drawing a black card in a single random draw from a well-shuffled deck of ordinary playing cards is \(\frac{1}{2}\) or 50%.

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