Concept explainers
a.
Find the
Check whether the probability changes for three tosses.
Find the probability of getting the first head in four tosses.
Mention the probability distribution of the given random variable r.
a.
Answer to Problem 19CRP
The probability of getting a head in the second trial is 0.25.
Yes, the probability change for three tosses is 0.125.
The probability of getting a head in the fourth toss is 0.0625.
The given random variable follows a geometric distribution with
Explanation of Solution
Geometric distribution:
- There should be n independent trials.
- Each trial has two outcomes.
- The probability of success is the same for each trial.
- The random variable n represents the number of trial in which the first success occurs.
The given random variable is based on getting the first head in tossing a coin and it satisfies the above conditions. Hence, it follows a geometric distribution.
The probability mass
Where,
From the given problem, the probability of getting a head while tossing a coin is 0.5. That is,
Therefore, the probability distribution of the given random variable n is
The probability of getting a head in the second trial is obtained below:
Therefore, the probability of getting a head in the second trial is 0.25.
The probability of getting a head in the third trial is obtained below:
Therefore, the probability of getting a head in the third trial is 0.125.
The probability of getting a head in the fourth trial is obtained below:
Therefore, the probability of getting a head in the fourth trial is 0.0625.
The given random variable follows a geometric distribution with
b.
Find the probability of getting a head in the fourth trail.
Find the probability of getting a head after four trials.
b.
Answer to Problem 19CRP
The probability of getting a head in the fourth trial is 0.0625.
The probability of getting a head after four trials is 0.0625.
Explanation of Solution
Calculation:
The probability of getting a head in the fourth trial is obtained below:
Therefore, the probability of getting a head in the fourth trial is 0.0625.
The probability of getting a head after four trials is obtained below:
Therefore, the probability of getting a head after four trials is 0.0625.
Want to see more full solutions like this?
Chapter 5 Solutions
Understandable Statistics: Concepts and Methods
- Flexible Work Hours In a recent survey, people were asked whether they would prefer to work flexible hours----even when it meant slower career advancement----so they could spend more time with their families. The figure shows the results of the survey. What is the probability that three people chosen at random would prefer flexible work hours?arrow_forwardIn Example 8, what is the probability that an employee chosen at random has 30 or more years of service?arrow_forwardIn Example 10, researchers selected five people at random from the population. What is the probability that all five people expected much of the workforce to be automated within 50 years?arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage