Question

2.In a study of pleas and prison sentences, it is found that 45% of the subjects studięd were sent to prison. Among those sent to prison, 40% plead guilty one of the study.bis tveef orteoreaho was fro wandatly stle dhe and je probe harine person was S FRZRent oaia esclecte, incthe gettn (4) If a study subject is randomly selected and it is then found that the šubject entéred á guilty plea, find the probability that this person was sent to prison

Answer 1

The probability of getting positive plead for randomly selected individual is,

P(G) P(G/P).P(P) P(G/P).P(P)

0.40 x 0.45+0.55 x 0.55

0.4825

Here we applying the Bay's theorem to determine the randomly selected person sent to prison. That is,

P(GandP) P(G)) T

P(P).P(G/P) P(G)

0.45 x 0.40 0.4825

0.3731