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Problem 1.27 State the exclusion-inclusion formula for P (U A,). A large and cheerful crowd of n junior wizards leave their staff in the Porter's Lodge on the way to a long night in the Mended Drum. On returning, each collects a staff at random from a pile, return to his room and attempts to cast a spell against hangovers. If a junior wizard attempts this spell with his own staff, there is a probability p that he will turn into a bullfrog. If he attempts it with someone else's staff, he is certain to turn into a bullfrog. Show that the probability that in the morning we will find n very surprised bullfrogs is approximately e-.

Problem 1.27 State the exclusion-inclusion formula for P (U A,). A large and cheerful crowd of n junior wizards leave their staff in the Porter's Lodge on the way to a long night in the Mended Drum. On returning, each collects a staff at random from a pile, return to his room and attempts to cast a spell against hangovers. If a junior wizard attempts this spell with his own staff, there is a probability p that he will turn into a bullfrog. If he attempts it with someone else's staff, he is certain to turn into a bullfrog. Show that the probability that in the morning we will find n very surprised bullfrogs is approximately e-.

Algebra & Trigonometry with Analytic Geometry
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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Problem 1.27 State the exclusion-inclusion formula for P (U, A,). A large and cheerful crowd of n junior wizards leave their staff in the Porter's Lodge on the way to a long night in the Mended Drum. On returning, each collects a staff at random from a pile, return to his room and attempts to cast a spell against hangovers. If a junior wizard attempts this spell with his own staff, there is a probability p that he will turn into a bullfrog. If he attempts it with someone else's staff, he is certain to turn into a bullfrog. Show that the probability that in the morning we will find n very surprised bullfrogs is approximately el-.
Transcribed Image Text:Problem 1.27 State the exclusion-inclusion formula for P (U, A,). A large and cheerful crowd of n junior wizards leave their staff in the Porter's Lodge on the way to a long night in the Mended Drum. On returning, each collects a staff at random from a pile, return to his room and attempts to cast a spell against hangovers. If a junior wizard attempts this spell with his own staff, there is a probability p that he will turn into a bullfrog. If he attempts it with someone else's staff, he is certain to turn into a bullfrog. Show that the probability that in the morning we will find n very surprised bullfrogs is approximately el-.
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