2. (20 pts.) Use the data in the accompanying table to answer the following ques

Question

2. (20 pts.) Use the data in the accompanying table to answer the following questions. Express the probability as a decimal with four digits after the decimal point, Show your work! Guilty Plea Plea of Not Guilty Sentenced to Prisorn Not Sentenced to Prison 578 a) If one of the 1028 subjects is randomly selected, find the 62 24 364 probability of selecting someone sentenced to prison. b) Find the probability of being sentenced to prison, given that the subject entered a plea of guilty c) Find the probability of being sentenced to prison, given that the subject entered a plea of not guilty d) After comparing the results of questions b and c, what do you conclude of wisdom of entering a guilty plea? e) If I of the subjects is randomly selected, find the probability of selecting someone who was sentenced to 0) If 2 different subjects are randomly selected, find the g) If 2 different subjects are randomly selected, find the h) If I of the subjects is randomly selected, find the prison or entered a plea of guilty probability that they both were sentenced to probability that they both entered pleas of not guilty probability of selecting someone who entered a plea of not prison . Ti guilty or was not sentenced to prison. i) If I of the subjects is randomly selected, find the probability of selecting someone who was sentenced to prison and entered a plea of guilty j) If I of the subjects is randomly selected, find the probability of selecting someone who was not sentenced to prison and did not entered a plea of guilty

Explanation / Answer

Answer:

1) Probability of selecting someone sentenced to prison = (364 + 62) / 1028 = 426/1028 = 0.414

2) Probability of being sentenced to prison, given that the subject entered a plea of guilty = 364/1028 = 0.354

3) Probability of being sentenced to prison, given that the subject entered a plea of not guilty = 62/1028 = 0.060

4) What do you conclude of wisdom of entering a guilty plea: The probability of sentencing to prison when subject entered a plea of guilty

5) Probability of selecting someone who was sentenced to prison or entered a plea of guilty: (364+62)/1028 + (364+578)/1028 - 364/1028 = 0.977

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