Chapter 7: Chapter 7

Student Admissions are based on the following table, which shows the profile, by the math section of the SAT Reasoning Test, of admitted students at UCLA for the Fall 2014 semester: \(^{44}\) SAT Reasoning Test-Math Section $$ \begin{array}{|r|c|c|c|c|c|c|} \hline & \mathbf{7 0 0 - 8 0 0} & \mathbf{6 0 0 - 6 9 9} & \mathbf{5 0 0 - 5 9 9} & \mathbf{4 0 0 - 4 9 9} & \mathbf{2 0 0 - 3 9 9} & \text { Total } \\ \hline \text { Admitted } & 8,398 & 3,517 & 1,410 & 358 & 9 & 13,692 \\ \hline \text { Not Admitted } & 16,599 & 18,363 & 13,119 & 6,714 & 1,652 & 56,447 \\ \hline \begin{array}{r} \text { Total } \\ \text { Applicants } \end{array} & 24,997 & 21,880 & 14,529 & 7,072 & 1,661 & 70,139 \\ \hline \end{array} $$ Determine the probabilities of the following events. (Round your answers to the nearest.01.) A rejected applicant had a Math SAT below 600 .

Two distinguishable dice are rolled. Could there be two mutually exclusive events that both contain outcomes in which the numbers facing up add to \(7 ?\)

Student Admissions are based on the following table, which shows the profile, by the math section of the SAT Reasoning Test, of admitted students at UCLA for the Fall 2014 semester: \(^{44}\) SAT Reasoning Test-Math Section $$ \begin{array}{|r|c|c|c|c|c|c|} \hline & \mathbf{7 0 0 - 8 0 0} & \mathbf{6 0 0 - 6 9 9} & \mathbf{5 0 0 - 5 9 9} & \mathbf{4 0 0 - 4 9 9} & \mathbf{2 0 0 - 3 9 9} & \text { Total } \\ \hline \text { Admitted } & 8,398 & 3,517 & 1,410 & 358 & 9 & 13,692 \\ \hline \text { Not Admitted } & 16,599 & 18,363 & 13,119 & 6,714 & 1,652 & 56,447 \\ \hline \begin{array}{r} \text { Total } \\ \text { Applicants } \end{array} & 24,997 & 21,880 & 14,529 & 7,072 & 1,661 & 70,139 \\ \hline \end{array} $$ Determine the probabilities of the following events. (Round your answers to the nearest.01.) A rejected applicant had a Math SAT of at least 600 .

According to The New York Times/CBS poll of March 2005 referred to in Exercise \(65,79 \%\) agreed that it should be the government's responsibility to provide a decent standard of living for the elderly, and \(43 \%\) agreed that it would be a good idea to invest part of their Social Security taxes on their own. What is the smallest percentage of people who could have agreed with both statements? What is the largest percentage of people who could have agreed with both statements?

Swords and Sorcery Lance the Wizard has been informed that tomorrow there will be a \(50 \%\) chance of encountering the evil Myrmidons and a \(20 \%\) chance of meeting up with the dreadful Balrog. Moreover, Hugo the Elf has predicted that there is a \(10 \%\) chance of encountering both tomorrow. What is the probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog?

A study shows that \(80 \%\) of the population was vaccinated against the Venusian flu but \(2 \%\) of the vaccinated population got the flu anyway. If \(10 \%\) of the total population got this flu, what percent of the population either got the vaccine or got the disease?

Compute the indicated quantity. \(P(A)=.5, P(B)=.4 . A\) and \(B\) are independent. Find \(P(A \mid B)\)

In Exercises \(9-18\) an experiment is given together with an event. Find the (modeled) probability of each event, assuming that the coins and dice are distinguishable and fair and that what is observed are the faces or numbers uppermost. (Compare with Exercises \(1-10\) in Section \(7.1 .)\) Two coins are tossed; the result is at most one tail.

Exercises \(7-12\) are based on the following table, which shows the frequency of outcomes when two distinguishable coins were tossed 4,000 times and the uppermost faces were observed. $$ \begin{array}{|r|c|c|c|c|} \hline \text { Outcome } & \text { HH } & \text { HT } & \text { TH } & \text { TT } \\ \hline \text { Frequency } & 1,100 & 950 & 1,200 & 750 \\ \hline \end{array} $$ What is the relative frequency that the second coin lands with heads up?

According to a study on the effect of music downloading on spending on music, \(11 \%\) of all Internet users had decreased their spending on music. \(^{69}\) We estimate that \(40 \%\) of all music fans used the Internet at the time of the study. \({ }^{70}\) If \(20 \%\) of non-Internet users had decreased their spending on music, what percentage of those who had decreased their spending on music were Internet users?