Question

1. Of the appliance repair shops listed in the phone book,
   80% are competent and 20% are not. A competent shop can repair an appliance correctly 95% of the time; an incompetent shop can repair an appliance correctly 60% of the time.
   Let C = { shop is competent }
         R = { shop can repair appliance correctly } and find the probability that:
   
   (a) the shop is incompetent, given that the appliance was repaired correctly
   (b) the shop is incompetent, given that the appliance was not repaired correctly
   Hint: Draw a probability tree and use Bayes' formula:
   
   

2 .Suppose P(E) = 0.2, P(F) = 0.4, and P(E | F) = 0.3. Find the following probabilities. (a) PE'| F=
(b) PE | F'=

Answer 1

Solutions 11 P (C) = 0.8 P =0.95 P ( A ) = 0.60 P(R) = P(E). P() + P 1 . P() 0.8 +0.64 0.2 = = 0.95% 0.88 P(R) P(R) = 0.6x0.2 0.88 0.1364 1 ay Play Planes PlEJ. PO oo*.2 - 10-1864) DP) PRA). PLO) (1-06) og = 10.6667 PIR) 1-0.88 0.6667

1 - 0.3 - 9) O PESO 1-P19) = 1-0.3 = 1017] b) PI & ) = P = TP (FC) PIEOFS = P1F) - P(EN F) = 0.4-0.3x0.4 1-0.4 - - 10.4667