If the probability of a new employee in a fast-food chain still being with the company at the end of the year is 0.5,what is the probability that out of 8 newly hired people(A) 5 will still be with the company after 1 year?(B) 5 or more will still be with the company after 1 year?Round each of the calculations to three decimal places when going through the solution process.(A) P(5 will still be there)~ (Round to three decimal places as needed.)DView an example Get more help.P PearsonhpClear allSaveCheck answerCopyright © 2022 Pearson Education Inc. All rights reserved. | Terms of Use | Privacy Policy | Permissions | Contact Us |

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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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1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.
K If the probability of a new employee in a fast-food chain still being with the company at the end of the year is 0.6, what is the probability that out of 8 newly hired people (A) 5 will still be with the company after 1 year? (B) 5 or more will still be with the company after 1 year? Round each of the calculations to three decimal places when going through the solution process. (A) P(5 will still be there) (Round to three decimal places as needed.)
Suppose I flip a fair coin n = 20 times. A psychic tries to predict the outcome before each flip. Three researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the psychic's success rate is 10%. Specifically: S+ 0 ~ U(.49, .51) M + 0 = .80 C0 = .10 %3D In all cases, assume the number of successful predictions follows a binomial distribution with success rate 0. Usek for the number of successes and n for the number of trials. Given all that: Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Morgan. Call that Bayes factor Bc:M Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over Sydney. Call that Bayes factor BM:S Determine the formula for the Bayes factor (a.k.a., likelihood…
Sarah and Thomas are going bowling. The probability that Sarah scores more than 175 is 0.5 , and the probability that Thomas scores more than 175 is 0.1 . Their scores are independent. Round your answers to four decimal places, if necessary. (a) Find the probability that both score more than 175 . (b) Given that Thomas scores more than 175 , the probability that Sarah scores higher than Thomas is 0.4 . Find the probability that Thomas scores more than 175 and Sarah scores higher than Thomas.
In this question, the real numbers in your answers should be given with three significant digits of accuracy after the decimal point. The public health authorities of a small town have divided the population into three categories: covid- negative, covid-positive, and hospitalised. After performing regular, extensive tests, they have observed that in each successive week: Among those who are negative, 95% remain so, 4% become positive, and 1% need to be hospitalised. • Among those who are positive, 75% recover and become negative, 20% stay positive, and 5% need to be hospitalised. Among those who are hospitalised, 60% recover and become negative, 30% are released from hospital but remain positive, and 10% remain hospitalised. (a) After representing the population in a given week as a column vector v = [n; p; h], where n, P, and h represent the number of people in the population who are negative, positive, and hospitalised respectively, write down a matrix M for which [n', p', h'] = M[n;…
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9. (a) What is the probability that he must stop at both signals? X (b) What is the probability that he must stop at the first signal but not at the second one? X (c) What is the probability that he must stop at exactly one signal?
You are allowed to take a certain test three times, and your final score will be the maximum of the test scores. Your score in test k, where k = 1, 2, 3, takes one of the values from k to 10 with equal probability 1/(11 − k), independently of the scores in other tests. What is the PMF of the final score?
Example 7.40: You set out on a walk with three possible locations, denoted locations 1, 2 and 3. The probabilities of travelling from a specified location to the next are given by Solution. If you know that you started in location 3, what is the probability that you end up at location 1 after two time periods? Using the above equation, we get To solve this we use the equation Xn+1 = AXn. Given that you began in location 3, the initial state vector is and subsequently Exercise X₁ = AX0 Probability = A = = X₂ = AX₁ 0.5 0.2 0.4 0.4 0.6 0.1 0.1 0.2 0.5 = Xo 0 0.5 0.2 0.4 0.4 0.6 0.1 0.2 0.5 0.1 ][ Therefore the probability of ending up in location 1 after two time periods is 0.42. 0.5 0.2 0.4 0.4 0.6 0.1 0.1 0.2 0.5 1 0.4 0.1 = 0.5 0.4 0.1 0.5 = 0.42 0.27 0.31 Refer to the example above. If you know that you started in location 2, what is the probability that you will end up at location 1 after one time period?
21 The Ebola virus has an infection rate of 11% per day as compared to the SARS virus, which has a rate of 4% per day. If there were one case of Ebola and 30 cases of SARS initially reported to authorities and cases are reported each day, which statement is true? At day 10 and day 53 there are more Ebola cases. (2) At day 10 and day 53 there are more SARS cases. (3) At day 10 there are more SARS cases, but at day 53 there are more Ebola cases. (4) At day 10 there are more Ebola cases, but at day 53 there are more SARS cases.

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