Basic Statistics20825 marksNumerical: Total probability theoremConditional probability and Bayes theorem
Three persons A, B, and C are being considered for appointment as Vice-Chancellor of a university, and whose chances of being selected are in the proportion 4:2:3 respectively. The probability that A, if selected, will introduce democratization is 0.3, and the corresponding probabilities for B and C
Three persons A, B, and C are being considered for appointment as Vice-Chancellor of a university, and whose chances of being selected are in the proportion 4:2:3 respectively. The probability that A, if selected, will introduce democratization is 0.3, and the corresponding probabilities for B and C are 0.5 and 0.8. What is the probability that democratization would be introduced? [5]
- Selection proportion for A : B : C = 4 : 2 : 3 - $P(D \mid A) = 0.3$ - $P(D \mid B) = 0.5$ - $P(D \mid C) = 0.8$ where $D$ = "democratization is introduced". Total parts $= 4 + 2 + 3 = 9$ $$P(A) = \frac{4}{9}, \quad P(B) = \frac{2}{9}, \quad P(C) = \frac{3}{9}$$ $$P(D) = P(DA)P(A) + P(DB)P(B) +...