Textbook Question
Notation When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P (M|B) represent? Is P (M|B) the same as P (B|M)?
Ch. 4 - Probability
Triola14th EditionElementary StatisticsISBN: 9780137366446
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Table of contents
- Ch. 1 - Introduction to Statistics88
- Ch. 2 - Exploring Data with Tables and Graphs70
- Ch. 3 - Describing, Exploring, and Comparing Data66
- Ch. 4 - Probability112
- Ch. 5 - Discrete Probability Distributions109
- Ch. 6 - Normal Probability Distributions122
- Ch. 7 - Estimating Parameters and Determining Sample Sizes107
- Ch. 8 - Hypothesis Testing75
- Ch. 9 - Inferences from Two Samples94
- Ch. 10 - Correlation and Regression80
- Ch. 11 - Goodness-of-Fit and Contingency Tables29
- Ch. 12 - Analysis of Variance42
Chapter 4, Problem 4.4.10
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?
Verified step by step guidance1
Step 1: Understand the structure of the call letters. Each call letter must begin with either 'K' or 'W', which gives us 2 choices for the first letter.
Step 2: Determine the number of additional letters. The problem states that there can be either 2 or 3 additional letters. Each additional letter can be any of the 26 letters in the English alphabet.
Step 3: Calculate the number of possibilities for 2 additional letters. For each of the 2 choices for the first letter ('K' or 'W'), there are 26 choices for the first additional letter and 26 choices for the second additional letter. The total number of possibilities for 2 additional letters is given by:
Step 4: Calculate the number of possibilities for 3 additional letters. Similarly, for each of the 2 choices for the first letter ('K' or 'W'), there are 26 choices for each of the 3 additional letters. The total number of possibilities for 3 additional letters is given by:
Step 5: Add the results from Step 3 and Step 4 to find the total number of possibilities. The total number of possibilities is:
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Combinatorics
Combinatorics is a branch of mathematics dealing with counting, arrangement, and combination of objects. In this context, it helps determine the number of possible combinations of letters that can form the call signs for radio stations. Understanding basic combinatorial principles, such as permutations and combinations, is essential for solving problems involving selection and arrangement.
Permutations and Combinations
Permutations refer to the different ways of arranging a set of items where the order matters, while combinations refer to the selection of items where the order does not matter. In the case of radio station call letters, we need to consider how many ways we can arrange the additional letters after the initial 'K' or 'W', which directly impacts the total number of unique call signs possible.
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Alphabetical Constraints
In this scenario, the call letters are constrained to the English alphabet, which consists of 26 letters. This limitation affects the total number of combinations possible for the additional letters in the call signs. Understanding how to apply these constraints is crucial for accurately calculating the total number of valid call letter combinations.
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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?
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Textbook Question
Soccer Shootout In the FIFA Women’s World Cup 2019, a tie at the end of two overtime periods leads to a “shootout” with five kicks taken by each team from the penalty mark. Each kick must be taken by a different player. How many ways can 5 players be selected from the 11 eligible players? For the 5 selected players, how many ways can they be designated as first, second, third, fourth, and fifth?
Textbook Question
In Exercises 9–12, assume that 100 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high.
75 girls.
Textbook Question
ZIP Code If you randomly select five digits, each between 0 and 9, with repetition allowed, what is the probability you will get the author’s ZIP code?
Textbook Question
In Exercises 33–40, use the given probability value to determine whether the sample results are significant.
Voting Repeat Exercise 33 after replacing 40 Democrats being placed on the first line of voting ballots with 14 Democrats being placed on the first line. The probability of getting a result as low as 14 is 0.029792.