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Chapter 5: Problem 21

In Problems \(21-24,\) a golf ball is selected at random from a golf bag. If the golf bag contains 9 Titleists, 8 Maxflis, and 3 Top-Flites, find the probability that the golf ball is: A Titleist or Maxfli.

Short Answer

Expert verified
The probability is \(\frac{17}{20}\).

Step by step solution

01

- Determine the total number of golf balls

Add up the total number of golf balls in the bag. The bag contains 9 Titleists, 8 Maxflis, and 3 Top-Flites.Total number of golf balls = 9 + 8 + 3.
02

- Calculate the total

Compute the total number of golf balls:Total golf balls = 20.
03

- Determine the number of favorable outcomes

Add the number of Titleists and the number of Maxflis because we are looking for the probability of drawing either a Titleist or a Maxfli:Number of Titleists = 9Number of Maxflis = 8Total favorable outcomes = 9 + 8.
04

- Calculate the number of favorable outcomes

Compute the total number of favorable outcomes:Total favorable outcomes = 17.
05

- Compute the probability

Use the probability formula to find the probability of drawing either a Titleist or a Maxfli:Probability = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)Probability = \(\frac{17}{20}\).

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Key Concepts

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

Random Selection
Random selection refers to choosing an item from a set without any bias. In probability theory, it's important because it ensures each item has an equal chance of being selected. For instance, in the exercise, we want to determine the probability of selecting a Titleist or Maxfli golf ball from a bag. Random selection means each of the 20 golf balls in the bag has an equal chance of being picked.
Favorable Outcomes
Favorable outcomes are the specific outcomes that meet the criteria of the event we're interested in. They are the desired results for which we're calculating the probability. In the given exercise, the favorable outcomes are drawing either a Titleist or a Maxfli golf ball. There are 9 Titleist and 8 Maxfli golf balls. So, the total number of favorable outcomes is 9 + 8 = 17.
Total Outcomes
Total outcomes represent all possible results of the random selection process. It's the complete set of outcomes we can get. For instance, in our golf bag, there are 20 golf balls (9 Titleists, 8 Maxflis, and 3 Top-Flites). Therefore, the total number of outcomes for drawing any golf ball is 20, as this includes all golf balls in the bag.
Probability Formula
The probability formula is a fundamental concept in probability theory used to calculate the likelihood of a specific event. The formula is given by:

\( \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \)
In the provided exercise, we applied this formula to find the probability of drawing a Titleist or Maxfli golf ball. Given 17 favorable outcomes and 20 total outcomes, the probability is \( \frac{17}{20} \), which simplifies to 0.85 or 85%. This means there's an 85% chance of picking either a Titleist or Maxfli golf ball from the bag.

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Most popular questions from this chapter

According to the U.S. National Center for Health Statistics, \(0.15 \%\) of deaths in the United States are 25 - to 34-year-olds whose cause of death is cancer. In addition, \(1.71 \%\) of all those who die are \(25-34\) years old. What is the probability that a randomly selected death is the result of cancer if the individual is known to have been \(25-34\) years old?

Adult Americans (18 years or older) were asked whether they used social media (Facebook, Twitter, and so on ) regularly. The following table is based on the results of the survey. $$ \begin{array}{lccccc} & \mathbf{1 8 - 3 4} & \mathbf{3 5 - 4 4} & \mathbf{4 5 - 5 4} & \mathbf{5 5 +} & \text { Total } \\ \hline \begin{array}{l} \text { Use social } \\ \text { media } \end{array} & 117 & 89 & 83 & 49 & \mathbf{3 3 8} \\ \hline \begin{array}{l} \text { Do not use } \\ \text { social media } \end{array} & 33 & 36 & 57 & 66 & \mathbf{1 9 2} \\ \hline \text { Total } & \mathbf{1 5 0} & \mathbf{1 2 5} & \mathbf{1 4 0} & \mathbf{1 1 5} & \mathbf{5 3 0} \\ \hline \end{array} $$ (a) What is the probability that a randomly selected adult American uses social media, given the individual is \(18-34\) years of age? (b) What is the probability that a randomly selected adult American is \(18-34\) years of age, given the individual uses social media? (c) Are 18 - to 34 -year olds more likely to use social media than individuals in general? Why?

In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, "When you see an ad emphasizing that a product is 'Made in America,' are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. $$ \begin{array}{lrrrrr} & \mathbf{1 8 - 3 4} & \mathbf{3 5 - 4 4} & \mathbf{4 5 - 5 4} & \mathbf{5 5 +} & \text { Total } \\ \hline \text { More likely } & 238 & 329 & 360 & 402 & \mathbf{1 3 2 9} \\ \hline \text { Less likely } & 22 & 6 & 22 & 16 & \mathbf{6 6} \\ \hline \begin{array}{l} \text { Neither more } \\ \text { nor less likely } \end{array} & 282 & 201 & 164 & 118 & \mathbf{7 6 5} \\ \hline \text { Total } & \mathbf{5 4 2} & \mathbf{5 3 6} & \mathbf{5 4 6} & \mathbf{5 3 6} & \mathbf{2 1 6 0} \end{array} $$ (a) What is the probability that a randomly selected individual is 35-44 years of age, given the individual is more likely to buy a product emphasized as "Made in America"? (b) What is the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in America," given the individual is \(35-44\) years of age? (c) Are 18 - to 34 -year-olds more likely to buy a product emphasized as "Made in America" than individuals in general?

According to the U.S. Census Bureau, the probability that a randomly selected household speaks only English at home is \(0.81 .\) The probability that a randomly selected household speaks only Spanish at home is 0.12 . (a) What is the probability that a randomly selected household speaks only English or only Spanish at home? (b) What is the probability that a randomly selected household speaks a language other than only English or only Spanish at home? (c) What is the probability that a randomly selected household speaks a language other than only English at home? (d) Can the probability that a randomly selected household speaks only Polish at home equal 0.08 ? Why or why not?

Because of a manufacturing error, three cans of regular soda were accidentally filled with diet soda and placed into a 12 -pack. Suppose that two cans are randomly selected from the 12 -pack. (a) Determine the probability that both contain diet soda. (b) Determine the probability that both contain regular soda. Would this be unusual? (c) Determine the probability that exactly one is diet and one is regular?
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