7. (10 2 marks each) In a study of pleas and prison sentences it is found that 4

Question

7. (10 2 marks each) In a study of pleas and prison sentences it is found that 45% of the subjects studied were sent to prison. Among sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plea guilty a. In this question the are two events, which well call A and B. i. Define event A 11 Define event B b. Draw a tree diagram showing the events, their compliments, and all associated probabilities. c. If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison.

Explanation / Answer

1)Event A is getting sent to prison

Event B is pleading guilty.

2) S

Prison(A) 0.45 Not Prison(Ac) 0.55

Guilty(B) Not Guilty(Bc) Guilty(B) Not Guilty(Bc)

0.45*0.4 0.45*0.6 0.55*0.55 0.55*0.45

3)Required probability = P(Ac) = 0.55

4) Required probabilty = 0.55*0.55 /[0.55*0.55 + 0.4*0.45] = 0.6269

5) Required probability = 0.55*0.45/[0.45*0.55+0.45*0.6] =0.4782

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.