Paul and Eric are playing squash, and Paul is determined to win at least two games.Unfortunately his chance of winning any one game is only, and this chance remains constanthowever many games he plays against Eric. The players agree to play 5 games and, if Paul haswon at least two by then, play ceases. Otherwise Paul persuades Eric to play a further 5 gameswith him. What is the probability(i) that only 5 games are played, and Paul wins at least two of them;(ii) that 10 games have to be played, and Paul wins at least two?

Answered: Image /qna-images/answer/651f9969-e568-401d-a172-d5695293cc67.jpg

Answered: Paul and Eric are playing squash, and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Three cowboys Doc Holiday, Wyatt Erp, and Wild Bill are locked in a 3-way duel. When the churchbell rings at high noon, all three will draw their guns and fire one shot simultaneously. A hit is registered if a shooter is hit by either of the other two cowboys. Doc Holiday will randomly aim and fire at either Wyatt Erp or Wild Bill, with an even split probability of 0.5 of who he'll shoot at. Being a good shot, he has a 60% chance of hitting the target he fires at. Wyatt Erp will randomly aim and fire at either Doc Holiday or Wild Bill, with an even split probability of 0.5 of who he'll shoot at. Also a good shot, he has a 60% chance of hitting the target he fires at. Wild Bill will randomly aim and fire at either Wyatt Erp or Doc Holiday, with an even split probability of 0.5 of who he'll shoot at. Being a poor shot, he only has a 30% chance of hitting the target he fires at. Let X denote the number of cowboys that are hit after all three take one shot at the same time. a) What are…
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Dubrovsky sits down to a night of gambling with his fellow officers. cach time he stakes u roubles there is a probability r that he will win and receive back 2u roubles (including his stake). At the beginning of the night he has 8000 roubles. If ever he has 256 000 roubles he will marry the beautiful Natasha and retire to his estate in the country. Otherwise, he will commit suicide. He decides to follow one of two courses of action: (i) to stake 1000 roubles each time until the issue is decided; (ii) to stake everything each time until the issue is decided. Advise him (a) if r= 1/4 and (b) if r=3/4. What are the chances of a happy ending in cach case if he follows your advice?

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