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Chapter 4: Problem 64
Find the joint probability of \(A\) and \(B\) for the following. a. \(P(A)=.36\) and \(P(B \mid A)=.87\) b. \(P(B)=.53\) and \(P(A \mid B)=.22\)
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Find \(P(A\) or \(B\) ) for the following. a. \(P(A)=.66, \quad P(B)=.47\), and \(P(A\) and \(B)=.33\) b. \(P(A)=.84, \quad P(B)=.61\), and \(P(A\) and \(B)=.55\)
An ice cream shop offers 25 flavors of ice cream. How many ways are there to select 2 different flavors from these 25 flavors? How many permutations are possible?
A consumer agency randomly selected 1700 flights for two major airlines, \(\mathrm{A}\) and \(\mathrm{B}\). The following table gives the two-way classification of these flights based on airline and arrival time. Note that "less than 30 minutes late" includes flights that arrived early or on time. $$ \begin{array}{lccc} \hline & \begin{array}{c} \text { Less Than 30 } \\ \text { Minutes Late } \end{array} & \begin{array}{c} \text { 30 Minutes to } \\ \text { 1 Hour Late } \end{array} & \begin{array}{c} \text { More Than } \\ \text { 1 Hour Late } \end{array} \\ \hline \text { Airline A } & 429 & 390 & 92 \\ \text { Airline B } & 393 & 316 & 80 \\ \hline \end{array} $$ If one flight is selected at random from these 1700 flights, find the following probabilities. a. \(P\) (more than 1 hour late or airline \(\mathrm{A}\) ) b. \(P(\) airline \(B\) or less than 30 minutes late) c. \(P(\) airline A or airline \(\mathrm{B}\) )
An appliance repair company that makes service calls to customers' homes has found that \(5 \%\) of the time there is nothing wrong with the appliance and the problem is due to customer error (appliance unplugged, controls improperly set, etc.). Two service calls are selected at random, and it is observed whether or not the problem is due to customer error. Draw a tree diagram. Find the probability that in this sample of two service calls a. both problems are due to customer error b. at least one problem is not due to customer error
How is the multiplication rule of probability for two dependent events different from the rule for two independent events?
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