I need help with this probability question. **Bayes Theorem**Let \( A \) and \( B \) be events in some sample space \( S \), where \( P(B) \neq 0 \), then we have\[P(A | B) = \frac{P(B | A) \cdot P(A)}{P(B | A) \cdot P(A) + P(B | \bar{A}) \cdot P(\bar{A})}\]The following example is taken from *The Pleasures of Probability* by Richard Issac.A man accused in a paternity case is found to have a genetic marker appearing in 1 percent of the adult male population. This genetic marker is found also in the child and could only be transmitted to the child through his father, with the child 100 percent certain of acquiring the marker if the father has it. The question is to determine the probability that the man is the father, given that the child has the genetic marker. In other words, we have CERTAIN evidence that the man has the genetic marker, we want to know what that evidence tells us about whether he is also the child's father (we also know the CHILD has the genetic marker too).**(Q1)** Before doing any analysis, **write down** what you think the probability that the man is the father, given that the child has the genetic marker.Recall it is KNOWN that the man has the genetic marker. Write down JUST what your intuition tells you. It does not matter if you are right or wrong, close or far away.Ask at least 5 other people the same question. You might put it this way, after reading them the paragraph above: Suppose you are a judge determining a paternity case, and you know all of the information given above together with two pieces of information: The man has the genetic marker and the child has the genetic marker. You must make your judgement based on this evidence and decide that given the child has the marker, what is the probability the MAN is his father.Write down your answer and the answers given by 5 other people (please read them the scenario above first, no need to try to explain probability or Bayes theorem, it is just their intuitive guess that we are concerned with here).Let \( A \) be the outcome that the man is the father, and let \( B \) be the outcome that the child has the marker.Let's use Bayes formula to calculate For now, we will assume three different values for P(A), and your job is to calculate, using Bayes' formula, the probability that given the child has the genetic marker, the man is the child's father (recall that it is certain that the man has the genetic marker).(Q2) Assume P(A) = 0.0005 (5 in 10000 chance the man is the father), calculate P(A | B) and report the value.(Q3) Assume P(A) = 0.005 (5 in 1000 chance the man is the father), calculate P(A | B) and report the value.(Q4) Assume P(A) = 0.05 (5 in 100 chance the man is the father), calculate P(A | B) and report the value.(Q5) Assume P(A) = 0.5 (5 in 10 chance the man is the father), calculate P(A | B) and report the value.(Q6) Go back to your original estimate. Which of the calculated values in (Q2) - (Q5) came closest to your estimate? Did you think that the chances of the man being the boy’s father were as low (or lower) than the assumed value of P(A)? Explain (in other words, write me a sentence or two explaining your thoughts, nothing is more boring than a yes or no answer).Note: For (Q2) - (Q5) use a calculator, but show your work in your upload. Be careful with order of operations (PEMDAS). When calculating a fraction it is best to place the numerator in parenthesis, and the denominator in parenthesis too.Remember that P(A) for any set A is always just a number between 0 and 1, inclusive. You are given two of those numbers above, and told the value of the 3rd, so you just need to use the rule for complimentary events to find the value of P(Ā) for each estimate of P(A) and you are ready start calculating.

As per our guidelines I can solve only first three subparts. Kindly post the remaining subparts…

For now, we will assume three different values for P(A), and your job is to calculate, using Bayes' formula, the probability that given the child has the genetic marker, the man is the child's father (recall the it is certain that the man has the genetic marker). (Q2) Assume P(A) = 0.0005 (5 in 10000 chance the man is the father), calculate P(A | B) and report the value. (Q3) Assume P(A) = 0.005 (5 in 1000 chance the man is the father), calculate P(A | B) and report the value. (Q4) Assume P(A) = 0.05 (5 in 100 chance the man is the father), calculate P( A | B) and report the value. (Q5) Assume P(A) = 0.5 (5 in 10 chance the man is the father), calculate P(A | B) and report the value. (Q6) Go back to your original estimate. Which of the calculated values in (Q2) - (Q5) came closest to your estimate? Did you think that the chances of the man being the boy's father were as low (or lower) than the assumed value of P(A)? Explain (in other words, write me a sentence or two explaining your thoughts, nothing is more boring than a yes or no answer). Note: For (Q2) - (Q5) use a calculator, but show your work in your upload. Be careful with order of operations (PEMDAS), When calculating a fraction it is best to place the numerator in parenthesis, and the denominator in parenthesis too. Remember that P(A) for any set A is always just a number between 0 and 1, inclusive. You are given two of those numbers above, and told the value of the 3rd, so you just need to use the rule for complimentary events to find the value of P(A) for each estimate of P(A) and you are ready start calculating.

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...