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Chapter 10: Problem 13

Arrange the following events from most likely to least likely. Explain your thinking a. being born right-handed b. flipping a single head if you flip a coin four times c. not watching any television this week d. being taller than the average class height e. no one being late to your math class this week

Short Answer

Expert verified
1a, 4d, 2b, 3c, 5e

Step by step solution

01

Identify Probabilities for Each Event

Let's assess the probability of each event mentioned in the options. 1. **Being born right-handed**: Approximately 90% of humans are right-handed.2. **Flipping a single head in four coin tosses**: Calculate using the binomial probability formula. The probability of getting exactly one head (H) in four flips of a fair coin (P(H)=0.5) is \( \binom{4}{1} imes (0.5)^1 imes (0.5)^3 = 4 imes 0.5 imes 0.125 = 0.25 \) or 25%.3. **Not watching any television this week**: This depends heavily on individual habits but generally speaking, it is less likely as most people watch some television during the week.4. **Being taller than the average class height**: By definition, about 50% of the people will be taller than the average height.5. **No one being late to math class this week**: This is quite variable and depends on class behavior, but it's reasonable to assume it's less likely than being right-handed.
02

Compare and Arrange Events Based on Probabilities

Given the estimated probabilities from Step 1, arrange the events: 1. **Being born right-handed** is the most likely event (90%). 2. **Being taller than the average class height** typically has about a 50% probability. 3. **Flipping a single head if you flip a coin four times** has a 25% chance. 4. **Not watching any television this week** is generally less likely compared to the others, varying heavily depending on individual habits. 5. **No one being late to your math class this week** is likely the least probable due to the number of students and the variability in attendance patterns.
03

Conclusion

The arrangement from most likely to least likely is: 1. Being born right-handed. 2. Being taller than the average class height. 3. Flipping a single head if you flip a coin four times. 4. Not watching any television this week. 5. No one being late to your math class this week.

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Key Concepts

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

Right-handedness
Being right-handed is highly common among humans. Approximately 90% of people are right-handed, which makes this trait much more prevalent than its left-handed counterpart. This high percentage implies that being born right-handed is one of the most likely events when considering probabilistic scenarios of everyday human traits.
  • High prevalence observed globally
  • Right-handedness often appears due to genetics and societal factors
  • This trait is a classic example of how probabilities manifest in natural human characteristics
Understanding that being right-handed is far more likely than not helps in comparing probable outcomes in different scenarios, aligning it as a cornerstone example when assessing probabilities across various events.
Binomial probability
When we talk about binomial probability, such as flipping a coin, we are dealing with events that have two possible outcomes. Consider the probability of getting a single head among four flips of a coin. Each flip is an independent event with a probability of 0.5 (or 50%) for landing heads.
Using the binomial formula, we find the probability of getting exactly one head out of four flips: \[ P(X=1) = \binom{4}{1} \times (0.5)^1 \times (0.5)^3 = 4 \times 0.5 \times 0.125 = 0.25 \] which equates to 25%. This calculated probability illustrates how specific outcomes can be precisely determined in controlled scenarios.
  • Understand "independent events" - result of one event does not affect the other
  • Grasp the concept of "binomial distribution" - focusing on scenarios with two outcomes
  • Real-life examples: lottery, survival rates
Television viewing habits
Viewing habits differ greatly among individuals, but a significant number of people do watch television regularly. Not watching any television at all in a week can be considered unusual in many cultures, although it heavily depends on lifestyle choices and preferences.
  • Individual preferences greatly affect viewing habits
  • Societal norms can also influence the likelihood of watching TV
  • Cultural differences impact overall statistics
Understanding the probability of individuals not watching TV helps cater specific assumptions made in statistical investigations, demonstrating how probabilities can change based on social and personal lifestyles.
Average class height
Being taller than the average class height implies a probability sitting around the 50% mark. By definition, the average, or mean, divides heights into two equal groups鈥攖aller and shorter. This demarcation means there's an equal chance of either being taller or shorter than the average.
  • Understanding "normal distribution" helps comprehend average-related probabilities
  • The use of "mean" to find central points of data
  • Class height examples show simple practical applications of average calculations
Recognizing average height probabilities makes educational data analyses in classroom settings more comprehensible, reflecting typical probability scenarios encountered in educational fun facts and studies.
Class attendance
Class attendance often includes variability depending on student habits, external conditions, and regularity. For no one to be late to class in a week, especially one involving multiple students, it's generally less likely given the numerous factors influencing attendance.
  • Diverse factors affect attendance: weather, personal issues, transport
  • Classroom dynamics and engagement influence punctuality
  • Statistical studies on attendance help identify patterns
Understanding attendance probabilities gives educators insight into potential barriers or issues within daily operations of education systems, emphasizing the importance of accommodating or anticipating potential delays or absences among students.

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Most popular questions from this chapter

Astrid works as an intern in a windmill park in Holland. She has learned that the anemometer, which measures wind speed, gives off electrical pulses and that the pulses are counted each second. The ratio of pulses per second to wind speed in meters per second is always \(4.5\) to 1 . a. If the wind speed is 40 meters per second, how many pulses per second should the anemometer be giving off? b. If the anemometer is giving off 84 pulses per second, what is the wind speed?

You have purchased 4 tickets to a school music department raffle. Three prizes will be awarded, and 150 tickets were sold. a. How many ways can the three prizes be assigned to the 150 tickets if the prizes are different? (a) b. How many ways can the three prizes be assigned to the 150 tickets if the prizes are the same?

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Sydney has one copy of each of the six Harry Potter books. a. In how many ways can Sydney's six books be arranged on a shelf? b. How many ways can the books be arranged so that Harry Potter and the Chamber of Secrets will be the rightmost book? c. Use the answers from \(6 \mathrm{a}\) and \(\mathrm{b}\) to find the probability that Harry Potter and the Chamber of Secrets will be the rightmost book if the books are arranged at random. d. What is the probability that the books will be in the exact order in which they were published? e. What is the probability that the books will not be in the exact order in which they were published? (T)
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