Question

A certain agency employs two consulting firms (A and B) with probabilities 0.60 and 0.4. respectively. From past experience, it is known that the probability of cost overruns alguns cas) for the firms is 0.05 and 0.1, respectively. a) What is the probability of cost overrune b) Suppose a cost overrun is experienced by the agency, what is the probability that the consulting firm involved is company Ba

Answer 1

Itis given that ,

$P(A)=0.6$

$P(B)=0.4$

Let L denotes the event that the company experiences cost overrun, it is given

$P(L|A)=0.05$

$P(L|B)=0.1$

a] the probability of cost overrun is

$P(L)=P(A)P(L|A)+P(B)P(L|B)$

  $=(0.05*0.6)+(0.1*0.4)=\boldsymbol{0.07}$

b] we need to find  

$P(B|L)=\frac{P(B)P(L|B)}{P(L)}$

$=\frac{0.1*0.4}{0.07}=\boldsymbol{\frac{4}{7}}$