25. Below are four short questions on probability, no two of which have the same correct answer. (No kidding.) Choose the question whose correct answer has the highest numerical value. (a) I have two children. What is the probability that the older one is a boy? (b) I have two children. Given that at least one of them is a boy, what is the probability that I have two boys? (c) I have two children. Given that at least one is a girl, what is the probability that I have two boys? (d) I have two children. Given that the older one is a boy born on Tuesday, what is the probability that I have two boys? These types of questions conventionally assume each child to be conceived as a boy or a girl with the exact 50-50 Markovian probability, independent of any previously conceived children.

25. Below are four short questions on probability, no two of which have the same correct answer. (No kidding.) Choose the question whose correct answer has the highest numerical value. (a) I have two children. What is the probability that the older one is a boy? (b) I have two children. Given that at least one of them is a boy, what is the probability that I have two boys? (c) I have two children. Given that at least one is a girl, what is the probability that I have two boys? (d) I have two children. Given that the older one is a boy born on Tuesday, what is the probability that I have two boys? These types of questions conventionally assume each child to be conceived as a boy or a girl with the exact 50-50 Markovian probability, independent of any previously conceived children.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section17.6: Absorbing Chains

Problem 7P

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Please help step by step with explanation for Program R (CS) with a final code for understanding thank you.
Q6/ The number of failures for a cryogenics machine from contamination in biological samples is a Poisson random variable with a mean of 0.01 per 100 samples. (a) If the lab usually processes 500 samples per day, what is the expected number of failures per day? (b) What is the probability that the machine will not fail during a study that includes 500 participants? (assume one sample per participant.) Ans. (0.05, 0.9512)
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A box contains three fair coins, and two trick coins that have heads on both sides.(a) What is the probability that a randomly selected coin from the box will come up heads whenflipped? (b) Suppose you randomly pick a coin from the box and flip it, and it comes up heads. What is theprobability that it’s one of the trick coins? (c) Let X be the random variable that represents the number of heads when every coin in the box isflipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes,or you can remember that coin flips are independent of each other.) (d) What is the expected number of heads when all the coins are flipped?Page 2
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