4. Probability

Counting

4. Probability

Counting

2:24 minutes

Problem 4.4.18

Textbook Question

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?

Verified step by step guidance

Step 1: Understand the problem. The goal is to calculate the probability that four golfers tee off in alphabetical order by last name. This involves determining the total number of possible orders and identifying the specific order that matches the alphabetical arrangement.

Step 2: Calculate the total number of possible orders. Since there are four golfers, the number of ways they can be arranged is given by the factorial of 4, denoted as 4!. The formula for factorial is n! = n × (n-1) × (n-2) × ... × 1. For 4 golfers, this would be 4 × 3 × 2 × 1.

Step 3: Identify the favorable outcome. There is only one specific arrangement where the golfers tee off in alphabetical order by last name. This is the favorable outcome.

Step 4: Calculate the probability. The probability of an event is given by the formula P(Event) = (Number of favorable outcomes) / (Total number of possible outcomes). Substitute the values: the number of favorable outcomes is 1, and the total number of possible outcomes is 4!.

Step 5: Simplify the expression. To find the probability, simplify the fraction using the value of 4! calculated earlier. This will give the final probability that the golfers tee off in alphabetical order by last name.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it quantifies the chance of the golfers teeing off in a specific order, which can be calculated by considering all possible arrangements of the golfers.

Permutations

Permutations refer to the different ways in which a set of items can be arranged in order. For four golfers, the total number of permutations is calculated as 4! (4 factorial), which equals 24. This concept is essential for determining the total possible outcomes when arranging the golfers.

Favorable Outcomes

Favorable outcomes are the specific outcomes that satisfy the condition of interest—in this case, the golfers teeing off in alphabetical order. Since there is only one specific arrangement that meets this criterion among the total permutations, understanding favorable outcomes is crucial for calculating the probability.

Watch next

Master Introduction to Permutations with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

Social Security Numbers A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security number of the person who was given the receipt?

Textbook Question

Quinela In a horse race, a quinela bet is won if you selected the two horses that finish first and second, and they can be selected in any order. The 144th running of the Kentucky Derby had a field of 20 horses. What is the probability of winning a quinela bet if you randomly select the horses?

Textbook Question

Radio Station Call Letters Radio and Television station call letters must begin with either K (for stations west of the Mississippi River) or W (for stations east of the Mississippi River) and must include either two or three additional letters. How many different possibilities are there?

Textbook Question

DNA Nucleotides DNA (deoxyribonucleic acid) is made of nucleotides. Each nucleotide can contain any one of these nitrogenous bases: A (adenine), G (guanine), C (cytosine), T (thymine). If one of those four bases (A, G, C, T) must be selected three times to form a linear triplet, how many different triplets are possible? All four bases can be selected for each of the three components of the triplet.

Textbook Question

Phone Numbers Current rules for telephone area codes allow the use of digits 2–9 for the first digit, and 0–9 for the second and third digits, but the last two digits cannot both be 1 (to avoid confusion with area codes such as 911). How many different area codes are possible with these rules? That same rule applies to the exchange numbers, which are the three digits immediately preceding the last four digits of a phone number. Given both of those rules, how many 10-digit phone numbers are possible? Given that these rules apply to the United States and Canada and a few islands, are there enough possible phone numbers? (Assume that the combined population is about 400,000,000.)

Textbook Question

Corporate Officers and Committees The Self Driving Unicycle Company was recently successfully funded via Kickstarter and must now appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO), and chief human resources officer (CHR). It must also appoint a strategic planning committee with five different members. There are 15 qualified candidates, and officers can also serve on the committee.

a. How many different ways can the five officers be appointed?

Textbook Question

b. How many different ways can a committee of five be appointed?

Textbook Question

ATM You want to obtain cash by using an ATM, but it’s dark and you can’t see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first.

a. What is the probability of selecting a random position and inserting the card with the result that the card is inserted correctly?

Show more practices