Question

The president of a company must decide which of two actions to take, say whether to rent or buy expensive machinery. Her vice-president is likely to make a faulty analysis and thus recommend the wrong decision with probability 0.05. The president hires two consultants who separately study the problem and make their recommendations. After watching them at work, the president estimates that one consultant is likely to recommend the wrong decision with probability 0.05, the other with probability 0.10. She decides to take the action recommended by a majority of the three reports she receives. What is the probability that she will make a wrong decision? Does the assumption of independence you have made seem reasonable in this problem?

Answer 1

the president will make wrong decision if at least two of three recommended wrong decision so

let vice president =VP consultant 1 =C1 consultant2=C2

required probability =P(at least two recommended wrong decision)

=P(VP and C1 wrong decision and C2 correct) +P(VP,C2 wrong decision and C1 correct) +P(VP correct decision and C1,C2 wrong decision) +P(all three gives wrong decision)

=0.05*0.05*0.9+0.05*0.1*0.95+0.95*0.05*0.1+0.05*0.05*0.1

=0.00225+0.00475+0.00475+0.00025=0.012

so probability that president makes wrong decision is 0.012

since VP ,C1 and C2 are indepenedent to each other so assumption of independence is reasonable in this problem