MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Concept explainers

Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…
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Only part C

c. Use the sample space to determine the exact probability that • Nobody gets the correct phone. • Exactly one person gets the correct phone. • Exactly two people get the correct phone. • All three people get the correct phone. • At least one person gets the correct phone. d. If this situation were to befall a group of five people, vou could calculate the probability that nobody gets the correct phone as 11/30, Explain in vour own words what this probability means about
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Transcribed Image Text:c. Use the sample space to determine the exact probability that • Nobody gets the correct phone. • Exactly one person gets the correct phone. • Exactly two people get the correct phone. • All three people get the correct phone. • At least one person gets the correct phone. d. If this situation were to befall a group of five people, vou could calculate the probability that nobody gets the correct phone as 11/30, Explain in vour own words what this probability means about
Random Cell Phones Suppose that three executives bump into each other in an elevator and drop their identical cellular phones as the doors are closing, leaving them with no alternative but to pick up a phone at random. a. Describe in detail how you could conduct a simulation of this situation to produce empirical estimates of the probabilities involved. Write the names of the three executives on 3 3 + index cards of the same size. Shuffle the cards well and deal them onto a sheet of paper on which you have drawn boxes - labeled with the names of the executives. Count how many matches you have between names on the index cards and names in the boxes. Record this value. Then reshuffle the cards and deal again. Repeat many times. The empirical estimate of the probability of one person getting their correct phone would be equal to the proportion of the times one match occurred divided by how many trials were run. Continuing this way we can form estimates for zero matches, two matches, and three matches. b. List all the possible outcomes in the sample space for this situation. For example, let 123 mean that the first cell phone went to the first executive, the second cell phone to the second executive, and the third cell phone to the third executive. In this case all three executives got their correct phone back. There are five other outcomes. 123, 132, 223, 232, 323, 332 123, 132, 213, 231, 312, 321 123, 133, 213, 233, 312, 322 123, 122, 211, 231, 322, 311 c. Use the sample space to determine the exact probability that Nobody gets the correct phone.
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Transcribed Image Text:Random Cell Phones Suppose that three executives bump into each other in an elevator and drop their identical cellular phones as the doors are closing, leaving them with no alternative but to pick up a phone at random. a. Describe in detail how you could conduct a simulation of this situation to produce empirical estimates of the probabilities involved. Write the names of the three executives on 3 3 + index cards of the same size. Shuffle the cards well and deal them onto a sheet of paper on which you have drawn boxes - labeled with the names of the executives. Count how many matches you have between names on the index cards and names in the boxes. Record this value. Then reshuffle the cards and deal again. Repeat many times. The empirical estimate of the probability of one person getting their correct phone would be equal to the proportion of the times one match occurred divided by how many trials were run. Continuing this way we can form estimates for zero matches, two matches, and three matches. b. List all the possible outcomes in the sample space for this situation. For example, let 123 mean that the first cell phone went to the first executive, the second cell phone to the second executive, and the third cell phone to the third executive. In this case all three executives got their correct phone back. There are five other outcomes. 123, 132, 223, 232, 323, 332 123, 132, 213, 231, 312, 321 123, 133, 213, 233, 312, 322 123, 122, 211, 231, 322, 311 c. Use the sample space to determine the exact probability that Nobody gets the correct phone.
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