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Answer:
(a) The probability of getting someone who was not sent to prison is 0.55.
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is 0.63.
Step-by-step explanation:
We are given that in a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
Let the probability that subjects studied were sent to prison = P(A) = 0.45
Let G = event that subject chose to plead guilty
So, the probability that the subjects chose to plead guilty given that they were sent to prison = P(G/A) = 0.40
and the probability that the subjects chose to plead guilty given that they were not sent to prison = P(G/A') = 0.55
(a) The probability of getting someone who was not sent to prison = 1 - Probability of getting someone who was sent to prison
P(A') = 1 - P(A)
= 1 - 0.45 = 0.55
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is given by = P(A'/G)
We will use Bayes' Theorem here to calculate the above probability;
P(A'/G) =
=
=
= <u>0.63</u>
Given:
Point = (8, 4)
To find:
The slope-intercept form of the equation of the line.
Solution:
Slope of this line = .
Slope of the line is same as the slope of .
Slope of the line (m) =
General form of line:
y = mx + b
---------- (1)
It contains the point (8, 4). Substitute x = 8 and y = 4 in (1).
Subtract 4 from both sides, we get
b = 0
Substitute b = 0 in (1).
Equation of the line:
<u>Complete the sentence:</u>
; I used the general form of a line in slope-intercept form, y = mx + b. The slope, m is
. Then I substituted 8 for x and 4 for y into the standard form and solved for b, which is 0.