Question

of the three men, the chances that of politician, a businessman, of an academician will be appointed as a vice-chancellor (vc) of a university are 0.5,0.3 and 0.2 respectively. Probability that the research is promoted to become vc of the university politician, businessman, and academician 0.3, 0.7, and 0.8 respectively. a) determine the probability that research is promoted. b) if reserch is promoted, what is the probability that vc is and academician?

Answer 1

Given,

P( politician is appointed as VC) = 0.5

P( businessman is appointed as VC) = 0.3

P( Academician is appointed as VC) = 0.2

P(Research is promoted | politician is appointed as VC) = 0.3

P(Research is promoted | businessman is appointed as VC) = 0.7

P(Research is promoted | academician is appointed as VC) = 0.8

a)

P( research is being promoted) = P( politician is appointed as VC)*P(Research is promoted | politician is appointed as VC) +

  P( businessman is appointed as VC)*P(Research is promoted | businessman is appointed as VC) +

  P( Academician is appointed as VC)*P(Research is promoted | academician is appointed as VC)

= 0.5*0.3 + 0.3*0.7 + 0.2*0.8 = 0.52

b)

This is done by Bayes theorem

P(academician is appointed as VC | research is promoted) =

P( Academician is appointed as VC)*P(Research is promoted | academician is appointed as VC) /

P( Research is promoted)

= ( 0.2*0.8)/0.52 = 0.3076923