2. An archer hits a bull's-eye with a probability of 0.09, and the results of different attempts can be taken to beindependent of each other. If the archer shoots nine arrows, calculate the probability that:(a) Exactly two arrows score bull's-eyes.(b) At least two arrows score bull's-eyes.(c) What is the expected number of bull's-eyes scored?

Solution: 2. Let X be the number of bull’s eyes scored and n be the sample number of arrows. From…

Answered: An archer hits a bull's-eye with a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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46 employees in an office wear eyeglasses. 34 have single-vision correction, and 12 wear bifocals. If two employees are selected at random from this group, what is the probability that both of them wear bifocals? What is the probability that both have single-vision correction? Round your answers to four decimal places. P(both employees wear bifocals)= i 0.1304 P(both employees have single-vision correction)= i 0.3736
Suppose the sensitivity of a diagnostic procedure to test whether a person has a particular disease is 95 % . A person who actually has the disease is tested for it using this procedure by two independent laboratories. (1) What is the probability that both test results will be positive? (ii) What is the probability that at least one of the two test results willI be positive?
The odds against the horse Bucksnot winning the race are 10:13. What is the probability that Bucksnot will win the race?
Based on long experience, an airline found that about 4% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 267 ticket reservations for an airplane with only 255 seats. (a) What is the probability that a person holding a reservation will show up for the flight?(b) Let n = 267 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. What expression represents the probability that a seat will be available for everyone who shows up holding a reservation? P(r ≥ 255)P(r ≤ 267) P(r ≥ 267)P(r ≤ 255) (c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? (Round your answer to four decimal places.)
The odds against the horse Bucksnot winning the race are 9:7. What is the probability that Bucksnot will win the race? Enter a reduced fraction
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 4 flights arrive on time. (b) Would it be unusual for Southwest to have 3 flights arrive late?(Enter YES or NO)
A fair die is rolled ten times. What is the probability of getting an even number 4 times out of 10? (3 d.p.)
: The probability that a mountain-bike rider travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: (a) exactly one has a burst tyre (b) at most three have a burst tyre (c) two or more have burst tyres.
The odds against the horse Bucksnot winning the race are 5:9. What is the probability that Bucksnot will win the race?
Based on long experience, an airline found that about 8% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 265 ticket reservations for an airplane with only 255 seats. (a) What is the probability that a person holding a reservation will show up for the flight? (b) Let n = 265 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. What expression represents the probability that a seat will be available for everyone who shows up holding a reservation? Select one of the options: P(r ≤ 255) P(r ≥ 255) P(r ≤ 265) P(r ≥ 265) (c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? (Round your answer to four decimal places.)
Overall, Steve Dalkowski throws a strike with 17% of his pitches (that is, the probability that he throws a strike with any given pitch is .17). (a) In one game, Dalkowski throws 240 pitches. What is the probability that he throws exactly 40 strikes? (b) In one week, Dalkowski throws 400 pitches. What is the probability that he throws 80 or more strikes? Every day for eternity Dalkowski throws 100 pitches, and records the number of strikes. (c) Find the mean µ, and the standard deviation o, of the numbers (of strikes thrown on different days) that Dalkowski records.
A large bank vault has several automatic burglar alarms. The probability is 0.55 that a single alarm will detect a burglar. (a) How many such alarms should be used to be 99% certain that a burglar trying to enter is detected by at least 8 alarm?

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