Question

Use the data in the table below to answer the questions that follow. Express each probability as a decimal carried out to 4 places. You must show your work to get credit.

(a) If one of the 1028 subjects is randomly selected, find the probability of selecting someone sentenced to prison.

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(b) Find the probability of being sentenced to prison, given that the subject entered a plea of guilty.

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(c) Find the probability of being sentenced to prison, given that the subject entered a plea of not guilty.

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(d) After comparing the results from questions b andc, what do you conclude about the wisdom of entering a guilty plea?

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(e) If one of the 1028 subjects is randomly selected, find the probability of selecting someone who was sentenced to prison or entered a guilty plea.

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(f) If two different subjects are randomly selected, find the probability that they both were sentenced to prison with no replacement.

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(g) If two different subjects are randomly selected, find that probability that they both entered pleas of not guilty with replacement.

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(h) If one of the 1028 subjects is randomly selected, find the probability of selecting someone who entered a plea of not guilty or was not sentenced to prison.

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	Guilty Plea	Not Guilty Plea
Sentenced to Prison	364	62
Not Sentenced to Prison	578	24

(i) If one of the 1028 subjects is randomly selected, find the probability of selecting someone who was sentenced to prison and entered a guilty plea.

                                                    __________________

(j) If one of the 1028 subjects is randomly selected, find the probability of selecting someone who was not sentenced to prison and did not enter a guilty plea.

                                                   __________________

Answer 1

a) P(sentenced to prison) = (364 + 62)/1028 = 426/1028 = 0.4144

b) P(sentenced to prison | plea of guilty) = P(sentenced to prison and plea of guilty)/P(lpea of guilty)

                                                                 = 364/(364 + 578) = 0.3864

c) P(sentenced to prison | plea of not guilty) = P(sentenced to prison and plea of not guilty)/P(plea of not guilty)

                                                                      = 62/(62 + 24)

                                                                      = 0.7209

e) P(sentenced to prison or guilty plea) = P(sentenced to prison) + P(guilty plea) - P(sentenced to prison and guilty plea) = (364 + 62)/1028 + (364 + 578)/1028 - 364/1028 = 0.9767

f) P(both are sentenced to prison) = 426C2/1028C2 = 0.1715

g) P(both are plea of not guilty) = 86/1028 * 86/1028 = 0.0070

h) P(not guilty plea or not sentenced to prison) = P(not guilty plea) + P(not sentenced to prison) - P(not guilty plea and not sentenced to prison) = (86 + 602 - 24)/1028 = 0.6459

i) P(sentenced to prison and guilty plea) = 364/1028 = 0.3541

j) P(not sentenced to prison and not guilty plea) = 24/1028 = 0.0233