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Chapter 4: Problem 49
A small ice cream shop has 10 flavors of ice cream and 5 kinds of toppings for its sundaes. How many different selections of one flavor of ice cream and one kind of topping are possible?
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Find \(P(A\) or \(B\) ) for the following. a. \(P(A)=.58, \quad P(B)=.66\), and \(P(A\) and \(B)=.57\) b. \(P(A)=.72, \quad P(B)=.42\), and \(P(A\) and \(B)=.39\)
Define the following two events for two tosses of a coin: \(A=\) at least one head is obtained \(B=\) both tails are obtained a. Are \(A\) and \(B\) mutually exclusive events? Are they independent? Explain why or why not. b. Are \(A\) and \(B\) complementary events? If yes, first calculate the probability of \(B\) and then calculate the probability of \(A\) using the complementary event rule.
An insurance company has information that \(93 \%\) of its auto policy holders carry collision coverage or uninsured motorist coverage on their policies. Eighty percent of the policy holders carry collision coverage, and \(60 \%\) have uninsured motorist coverage. a. What percentage of these policy holders carry both collision and uninsured motorist coverage? b. What percentage of these policy holders carry neither collision nor uninsured motorist coverage? c. What percentage of these policy holders carry collision but not uninsured motorist coverage?
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. $$\begin{array}{lccc} & \begin{array}{c} \text { Less Than 30 } \\ \text { Minutes Late } \end{array} & \begin{array}{c} 30 \text { Minutes to } \\ \text { 1 Hour Late } \end{array} & \begin{array}{c} \text { More Than } \\ \text { 1 Hour Late } \end{array} \\ \hline \text { Airline A } & 429 & 390 & 92 \\ \text { Airline B } & 393 & 316 & 80 \end{array}$$ If one flight is selected at random from these 1700 flights, find the following probabilities. a. \(P(\) more than 1 hour late or airline \(A\) ) b. \(P(\) airline \(\mathrm{B}\) or less than 30 minutes late) c. \(P(\) airline A or airline \(\mathrm{B}\) )
Given that \(A\) and \(B\) are two independent events, find their joint probability for the following. a. \(P(A)=.61\) and \(P(B)=.27\) b. \(P(A)=.39\) and \(P(B)=.63\)
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