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Chapter 4: Problem 22

2014 Top Albums (Based on U.S. sales) Of all of the U.S. album sales 1989 (Taylor Swift) accounted for \(25 \%\) of sales, Frozen (Various Artists) accounted for \(24.1 \%\) of sales, In the Lonely Hour (Sam Smith) accounted for \(8.2 \%\) of sales. What is the probability that a randomly selected album was something other than these three albums?

Short Answer

Expert verified
The probability is 0.427.

Step by step solution

01

Identify Given Percentages

We are given the percentages of U.S. album sales for three albums: '1989' by Taylor Swift accounts for 25%, 'Frozen' by Various Artists accounts for 24.1%, and 'In the Lonely Hour' by Sam Smith accounts for 8.2%.
02

Calculate Total Percentage of Given Albums

To find the total percentage of album sales for these three albums, add their individual percentages:\[25\% + 24.1\% + 8.2\% = 57.3\%\] This means the combined album sales for these three is 57.3% of the total.
03

Determine Percentage of Other Albums

If these three albums account for 57.3% of sales, the remaining percentage is accounted for by other albums. Calculate this by subtracting from 100%:\[100\% - 57.3\% = 42.7\%\] Thus, 42.7% of the sales are from albums other than these three.
04

Calculate Probability

Convert the percentage of sales from albums other than the given three into a probability. Since the percentage is 42.7%, the probability that a randomly selected album was something other than these three is 0.427.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Percentages in Album Sales
Percentages play a crucial role in interpreting data, such as album sales. A percentage represents a fraction of 100 and helps compare parts of a whole in a straightforward way.
Imagine you have 100 albums sold in the U.S., and '1989' by Taylor Swift accounts for 25 of these sales. This means '1989' captures 25% of the market share for that time.
Similarly, 'Frozen' covers 24.1%, and 'In the Lonely Hour' contributes 8.2%. Adding them up gives us the total market share for these albums.
  • Total percentage for these three albums: 25% + 24.1% + 8.2% = 57.3%
This shows that a significant portion of sales belonged to these few popular albums.
Impact of Popular Albums on Sales
Popular albums like '1989', 'Frozen', and 'In the Lonely Hour' can dominate sales charts significantly.
This phenomenon is common in the music industry, where certain albums capture a large audience share.
Sales percentages showcase how much impact a particular album has within the market.
  • Large sales percentages usually equate to millions of copies sold.
  • Albums with high percentages garner more attention from media and fans.
These top albums not only reflect artist popularity but also influence market trends and future album productions.
Steps to Calculate Probability from Percentages
Transforming percentages into probability is simple and essential for understanding likelihoods.
Probability expresses how likely an event is to happen; it ranges from 0 to 1. For instance, the probability that a randomly-selected item fits your criteria.
To calculate probability based on percentages, follow these steps:
  • First, determine the total percentage relevant to your criteria by adding individual percentages.
  • Subtract this total from 100% to find the percentage of the opposite criteria.
  • Finally, convert this percentage into a decimal for the probability. For example, 42.7% becomes 0.427.
This process helps in understanding how often different events occur in diverse scenarios.
The Role of Elementary Statistics in Analyzing Data
Elementary statistics provide the foundation to analyze and interpret data effectively.
With statistics, we can break down complex data like album sales into digestible parts.
The core ideas involve understanding basic principles, like calculating percentages and probabilities.
  • Help us draw meaningful conclusions from numerical data.
  • Enable decision making through the interpretation of collected information.
Statistics encourage a deeper insight into the data that moves beyond mere numbers, revealing patterns and trends.

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Most popular questions from this chapter

$$ \begin{array}{l}{\text { Odds Odds are used in gambling games to make them }} \\\ {\text { fair. For example, if you rolled a die and won every }} \\\ {\text { time you rolled a } 6, \text { then you would win on average }} \\\ {\text { once every } 6 \text { times. So that the game is fair, the odds of }} \\ {5 \text { to } 1 \text { are given. This means that if you bet } \$ 1 \text { and won, }} \\ {\text { you could win } \$ 5 . \text { On average, you would win } \$ 5 \text { once }} \\ {\text { in } 6 \text { rolls and lose } \$ 1 \text { on the other } 5 \text { rolls-hence the }} \\ {\text { term fair game. }}\end{array} $$ $$ \begin{array}{l}{\text { In most gambling games, the odds given are not fair. }} \\ {\text { For example, if the odds of winning are really } 20 \text { to } 1,} \\ {\text { the house might offer } 15 \text { to } 1 \text { in order to make a profit. }} \\ {\text { Odds can be expressed as a fraction or as a ratio, }} \\ {\text { such as } \frac{5}{1}, 5: 1, \text { or } 5 \text { to } 1 . \text { Odds are computed in favor }} \\ {\text { of the event or against the event. The formulas for }} \\ {\text { odds are }}\end{array} $$ $$ \begin{array}{l}{\text { Odds in favor }=\frac{P(E)}{1-P(E)}} \\ {\text { Odds against }=\frac{P(\bar{E})}{1-P(\bar{E})}}\end{array} $$ In the die example, $$ \begin{array}{c}{\text { Odds in favor of a } 6=\frac{\frac{1}{6}}{\frac{5}{6}}=\frac{1}{5} \text { or } 1: 5} \\ {\text { Odds against a } 6=\frac{\frac{5}{6}}{\frac{1}{6}}=\frac{5}{1} \text { or } 5: 1}\end{array} $$ Find the odds in favor of and against each event. a. Rolling a die and getting a 2 b. Rolling a die and getting an even number c. Drawing a card from a deck and getting a spade d. Drawing a card and getting a red card e. Drawing a card and getting a queen f. Tossing two coins and getting two tails g. Tossing two coins and getting exactly one tail

Licensed Drivers in the United States In a recent year there were the following numbers (in thousands) of licensed drivers in the United States. $$ \begin{array}{lll}{} & {\text { Male }} & {\text { Female }} \\ \hline \text { Age 19 and under } & {4746} & {4517} \\ {\text { Age } 20} & {1625} & {1553} \\ {\text { Age } 21} & {1679} & {1627}\end{array} $$ Choose one driver at random. Find the probability that the driver is a. Male and 19 years or under b. Age 20 or female c. At least 20 years old

Rolling Two Dice If two dice are rolled one time, find the probability of getting these results: a. A sum of 5 b. A sum of 9 or 10 c. Doubles

Seating in a Movie Theater How many different ways can 5 people- \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D},\) and \(\mathrm{E}-\) sit in a row at a movie theater if \((a) \mathrm{A}\) and \(\mathrm{B}\) must sit together; \((b) \mathrm{C}\) must sit to the right of, but not necessarily next to, \(\mathrm{B} ;(c) \mathrm{D}\) and \(\mathrm{E}\) will not sit next to each other?

Family Dinner Combinations A family special at a neighborhood restaurant offers dinner for four for \(\$ 39.99\). There are 3 appetizers available, 4 entrees, and 3 desserts from which to choose. The special includes one of each. Represent the possible dinner combinations with a tree diagram.
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