Question

In: Statistics and Probability

12. For a-j below, use the data in the table below which details the value of...

12. For a-j below, use the data in the table below which details the value of pleading guilty versus not guilty in criminal courts and the judicial sentencing thereafter. Express all probabilities as decimals rounded to four places (when possible). Guilty Plea Plea of Not Guilty Sentenced to Prison 392, 58. Not Sentenced to Prison 564, 14.

a. If one (1) of the 1028 subjects is randomly selected, find the probability of selecting someone sentenced to prison.

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

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

d. Based on the results from b & c, what conclusions would you make about the wisdom of entering a guilty plea?

e. If one (1) of the 1028 subjects is randomly selected, find the probability of selecting someone who was sentenced to prison or entered a plea of guilty.

f. If two (2) different study subjects are randomly selected, find the probability that they were both sentenced to prison.

g. Find the probability of randomly selecting 1 of the 1028 subjects and getting a subject who was sentenced to prison and entered a guilty plea.

Expert Solution

	Guilty Plea	Plea of no Guilty	Total
Sentenced to prison	392	58	450
Not sentenced to prison	564	14	578
	956	72	1028

a) the probability of selecting someone sentenced to prison.=

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

The required probability =

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

The required probability =

d) A person is less likely to be sentenced to prison if he enters a guilty plea and more likely to be sentenced to prison if he enters the non-guilty plea.

e) the probability of selecting someone who was sentenced to prison or entered a plea of guilty. =

orchestra answered 2 years ago

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