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Chapter 2: Problem 91

Find the probability of drawing a spade on a single random draw from a well- shuffled deck of cards.

Short Answer

Expert verified
The probability of drawing a spade on a single random draw from a well-shuffled deck of cards is \(\frac{1}{4}\), which is equivalent to 0.25 or 25%.

Step by step solution

01

Identify the number of spade cards in the deck

There are 13 spade cards in a standard deck of 52 playing cards. These 13 cards consist of A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, and K, all of which belong to the spade suit.
02

Identify the total number of cards in the deck

In a standard deck of playing cards, there are 52 cards. These are divided into 4 suits (spades, hearts, diamonds, and clubs), each with 13 cards.
03

Calculate the probability

To find the probability of drawing a spade on a single random draw from the deck, we need to divide the number of spade cards in the deck by the total number of cards in the deck. Using the formula for probability: Probability = \(\frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}}\) In this case, the number of successful outcomes is the number of spade cards (13), and the total number of possible outcomes is the total number of cards in the deck (52). Plugging these values into the formula, we get: Probability = \(\frac{13}{52}\)
04

Simplify the fraction

Now, we need to simplify the fraction. Both 13 and 52 are divisible by 13: \(\frac{13}{52} = \frac{13 \div 13}{52 \div 13} = \frac{1}{4}\)
05

Interpret the result

Thus, the probability of drawing a spade on a single random draw from a well-shuffled deck of cards is \(\frac{1}{4}\) or 0.25 or 25%. This means that, on average, one out of every four card draws will be a spade.

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Most popular questions from this chapter

Calculate the number of permutations of the letters \(\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\) taken two at a time.

Determine the number of permutations of the letters in the word BANANA.

A bag contains 4 white balls, 6 black balls, 3 red balls, and 8 green balls. If one ball is drawn from the bag, find the probability that it will be either white or green.

Find the probability of throwing at least one of the following totals on a single throw of a pair of dice: a total 5 , a total of 6 , a total of 7 . Define the events \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\) as follows: Event A: a total of 5 is thrown, Event \(B\) : a total of 6 is thrown, Event C: a total of 7 is thrown.

Find the probability that Event \(\mathrm{A}\), drawing a spade on a single draw from a deck of cards, and Event \(B\), rolling a total of 7 on a single roll of a pair of dice, will both occur.
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