Question

Express the probability as a decimal with four digits after the decimal point. Show your work!

	Guilty Plea	Plea of Not Guilty
Sentenced to Prison	367	68
Not Sentenced to Prison	572	36

If one of the 1043 subjects is randomly selected, find the probability of selecting someone sentenced to prison.

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

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

After comparing the results of questions b and c, what do you conclude of wisdom of entering a guilty plea?

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

If 2 different subjects are randomly selected, find the probability that they both were sentenced to prison.

If 2 different subjects are randomly selected, find the probability that they both entered pleas of not guilty.

If 1 of the subjects is randomly selected, find the probability of selecting someone who entered a plea of not guilty or was not sentenced to prison.

If 1 of the subjects is randomly selected, find the probability of selecting someone who was sentenced to prison and entered a plea of guilty.

If 1 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.

 

Answer 1

1)If one of the 1043 subjects is randomly selected, find the probability of selecting someone sentenced to prison.

=(367+68)/1043

=435/1043

=0.417

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

P(a)=being sentenced to prison =0.417

P(b)=subject entered a plea of guilty =(367+572)/1043 =0.9

P(a n b) =367/1043. =0.3518

P(a|b)=p(a n b)/p(b)

=0.3518/0.9

=0.3909

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

p(a) =beaing sentenced to prison=0.417

p(b)=subject entered a plea of not guilty =68+36/1043 =0.0997

p(a n b)=68/1043 =0.065

p(a|b)=p(a n b)/p(b)

=0.065/0.0997

=0.6539

1 of the subjects is randomly selected, find the probability of selecting someone who was sentenced to prison or entered a plea of guilty

=367+68+572/1043

=1007/1043

=0.965

If 2 different subjects are randomly selected, find the probability that they both were sentenced to prison.

=(435/1043)*(435/1043)

=0.1739

2 different subjects are randomly selected, find the probability that they both entered pleas of not guilty.

=(104/1043)*(104/1043)

=0.0099