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If one survey response was randomly selected, what is the probability that it was given by a female?
If two responses were randomly selected, one at a time, without replacement, what is the probability that both were given by a male?
What is the probability that a selection was over 64 dollars, given that it was a response from a female?
What is the probability that a single random selection was over 64 dollars no matter if a male or a female made the selection?
Search the internet for an article published in the last 18 months on how businesses use probability. Provide the title, author, and the URL. Provide a two-sentence summary of how probability is used in business.

  1. Suppose that a couple will have three children. Let B represent a boy and let G represent a girl. Draw a tree diagram depicting the sample space outcomes for this experiment.
  2. Explain what it means for two events to be mutually exclusive.
  3. Explain what it means for two events to be independent.
  4. Explain the purpose of Bayes’ Theorem.
  5. Explain how the values of a discrete random variable differ from the values of a continuous random variable.
  6. Classify each of the following random variables as discrete or continuous.

a. X = the number of girls born to a couple with three children

b. X = the number of defects found on a car at a final inspection

c. X = the number of incorrect lab procedures conducted at a hospital during a given week

d. X = the time needed by a clerk to complete a task

e. X = the temperature of a pizza at a given time

  1. List and explain the characteristics of a binomial experiment

Sample Solution

In reviewing the case, the Court examined whether the state had a compelling interest to exclude and intern anyone of Japanese ancestry. The majority argued that pressing public necessity could justify racial restrictions when pure racial antagonism cannot (Choper, Fallon, Kamisar, and Shiffrin, 1202). They claimed national security was a compelling interest and that the military and congress acted constitutionally in creating the internment order. Ultimately, the majority concluded that national security concerns was a compelling enough interest to overcome the very strong presumption of unconstitutionality incorporated in strict scrutiny, the standard of review the majority claims to apply. Although the majority opinion spends a good deal of time explaining the state had a compelling interest, they barely address the part of strict scrutiny requiring the legislative means be narrowly tailored to the legislative ends. The only statement that vaguely addresses it is when Black writes that interning Japanese has a clear and close relationship to stopping espionage (Choper, Fallon, Kamisar, and Shiffrin, 1202). In my opinion, the Court could not have upheld the legislative classification interning people of Japanese ancestry if strict scrutiny had truly been applied. Consequently, rational basis must have been the standard of review used. First off, the Court deferred to other branches of government in making their decision, which seems to imply rational basis rather than strict scrutiny. In the majority opinion, Black specifically writes that the war making branches of government had "ground" to create the internment order. However, "having ground" for a legislative classification is much closer to the language of rational basis, which requires the person challenging the legislation to show state lacks a legitimate interest and the legislative means are not rationally related to the legislative ends. Secondly, I don't believe the state actually had a compelling interest in making the legislation and therefore the Court must have applied rational basis in order to uphold Executive Order 9066. As Justice Murphy writes in his dissent, not one person of Japanese ancestry was tried or convicted for espionage while they were free in the time between the Pearl Harbor attack and the internment (Choper, Fallon, Kamisar, and Shiffrin, 1203). Illustrating my point that the state certainly did not have a compelling interest to make legislation interning Japanese Americans. Although the
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