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Chapter 4: Q18 (page 175)

In Exercises 5–36, express all probabilities as fractions.

Teed Off When four golfers are about to begin a game, they often toss a tee to randomly select the order in which they tee off. What is the probability that they tee off in alphabetical order by last name?

Short Answer

Expert verified

The probability that the golfers tee off in alphabetical order by the last name is 124.

Step by step solution

01

Given information

Four golfers toss a tee to decide the order in which they tee off.

02

Define factorial

The total number of possible arrangements of a given set of units (n) is computed using thefactorialformula.

n!=n×n-1×n-2×...1

03

Calculation

Let A be the event that the golfers tee off in alphabetical order of the last name.

The total number of ways in which they can tee off is calculated below:

4!=4×3×2×1=24

The number of ways in which they can tee off in alphabetical order is one.

The probability that the golfers tee off in alphabetical order of the last name

PA=NumberoffavourablewaysTotalnumberofways=124

Therefore, the probability that the golfers tee off in alphabetical order of the last name is equal to 124.

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Most popular questions from this chapter

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a. What is the probability that Mike will guess correctly? (Ignore leap years.)

b. Would it be unlikely for him to guess correctly on his first try?

c. If you were Kelly, and Mike did guess correctly on his first try, would you believe his claim that he made a lucky guess, or would you be convinced that he already knew when you were born?

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Purchased Gum

Kept the Money

Students Given Four Quarters

27

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Students Given a $1 bill

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Denomination Effect

a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.

b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.

c. What do the preceding results suggest?
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