Question

In a study of pleas and prison​ sentences, it is found that 6060​% of the subjects studied were sent to prison. Among those sent to​ prison, 4646​% choose to plead guilty. Among those not sent to​ prison, 3636​% choose to plead guilty. a. If one of the study subjects is randomly​ selected, find the probability of getting someone who was not sent to prison. b. If a study subject is randomly selected and it is then found that the subject entered a guilty​ plea, find the probability that this person was not sent to prison.

Answer 1

Answer:

a. 40 %

b. 34.3 % ( approx )

Step-by-step explanation:

Let S is the event of the subjects studied that were sent to prison,

S' is the event of the subjects studied that won't sent to prison,

G is the event of pleading guilty,

G' is the event of not pleading guilty,

According to the question,

P(S) = 60% = 0.6 ⇒ P(S') = 1 - P(S) = 1 - 0.6 = 0.4,

P(S∩G) = 46% of 60% = 0.46 × 0.60 = 0.276,

P(S'∩G) = 36% of 40% = 0.36 × 0.40 = 0.144,

P(G) = P(S∩G) + P(S'∩G) = 0.276 + 0.144 = 0.42

a. The of getting someone who was not sent to prison, P(S') = 0.4,

b. the probability that this person was not sent to prison when it is given that the subject entered a guilty​ plea,

$P(\frac{S'}{G})=\frac{P(S'\cap G)}{P(G)}=\frac{0.144}{0.42}\approx 0.343=34.3\%$