Assume that Pr[E]=0.55, Pr[F]=0.55, Pr[G]=0.45, Pr[E∪F]=0.8,Pr[E∪G]=0.75, and Pr[F∪G]=0.75. Find the following probabilities: (1) Pr[E′∪F]=Pr[E′∪F]= (2) Pr[F′∩G]=Pr[F′∩G]= (3) Pr[E∩G]=Pr[E∩G]=

Assume that Pr[E]=0.55, Pr[F]=0.55, Pr[G]=0.45, Pr[E∪F]=0.8,Pr[E∪G]=0.75, and Pr[F∪G]=0.75. Find the following probabilities: (1) Pr[E′∪F]=Pr[E′∪F]= (2) Pr[F′∩G]=Pr[F′∩G]= (3) Pr[E∩G]=Pr[E∩G]=

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 30E

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

Assume that Pr[E]=0.55, Pr[F]=0.55, Pr[G]=0.45, Pr[E∪F]=0.8,Pr[E∪G]=0.75, and Pr[F∪G]=0.75. Find the following probabilities:

(1) Pr[E′∪F]=Pr[E′∪F]=

(2) Pr[F′∩G]=Pr[F′∩G]=

(3) Pr[E∩G]=Pr[E∩G]=

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