Lottery Prizes A lottery offers one $800 prize, one $600 Prize, two $400 prizes, and four $200 prizes. One thousand tickets are sold at $6 each. Find the expectation if a person buys five tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round

Lottery Prizes A lottery offers one $800 prize, one $600 Prize, two $400 prizes, and four $200 prizes. One thousand tickets are sold at $6 each. Find the expectation if a person buys five tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.4: Expected Value

Problem 15E: A Game of Chance A box contains 100 envelopes. Ten envelopes contain $10 each, ten contain $5 each,...

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A Game of Chance A box contains 100 envelopes. Ten envelopes contain $10 each, ten contain $5 each, two are “unlucky", and the rest are empty. A player draws an envelope from the box and keeps whatever is in it. If a person draw an unlucky envelope, however, he must pay $100. What is the expectation of a person playing this game?
Combination Lock A safe containing $1000000 is locked with a combination lock. You pay $1 for guess at the six- digit combination. If open the lock, you get to keep the million dollars. What is expectation?
Monkeys Typing Shakespeare An often-quoted example of an event of extremely low probability is that a monkey types Shakespeare’s entire play Hamlet by randomly striking keys tin a typewriter. Assume that the typewriter has 48 keys (including the space bar) and that the monkey is equally likely lo hit any key. Find the probability that such a monkey will actually correctly type just the title of the play as his first word. What is the probability that the monkey will type the phrase "To be or not to be" as his first words?
Backup Vehicle A fire department keeps two rescue vehicles. Due to the demand on the vehicles and the chance of mechanical failure, the probability that a specific vehicle is available when needed is 90%. The availability of one vehicle is independent of the availability of the other. Find the probability that (a) both vehicles are available at a given time, (b) neither vehicle is available at a given time, and (c) at least one vehicle is available at a given time.
Backup System A space vehicle has an independent backup system for one of its communication networks. The probability that either system will function satisfactorily during a flight is 0.985 what is the probability that during a given flight (a) Both systems function satisfactorily, (b) Both systems fail, and (c) At least one system functions satisfactorily?