Question

Question 1 In certain city, there are two cab companies, the blue cabs, which own 70 % of the cabs, and the green cabs, which own 30 %. A cab involved in a hit and run accident and a witness says she thought it was a green one. Tests were made and it was found she could correctly identify the colour of the cab 60% of the time in the lighting conditions under which the accident took place, 40% of the time she mistakenly thought a blue cab was green. Whether the cab in the accident is more likely to have been blue or green. 15 marks

Answer 1

Lad, dhe accident E, Cab im blue is accidamt is E Cab in ean hat the Cab witmers said A = One reen was PCE)30 30 100 PCA/E) Probabilit dhat withnes dheught the that tha given Cab to be blue Cobs was 40 witnos thoreg t the that dhe that plA/EPrehahilty to be grraan graam iuon Cecb Cab was 6 Theooram, .. PCEP CA/E) pLE/A)= P(E) P(A/E + PlE PCA/E 28 28 14 28t18 23 10 T0

amd PCE, x PCA/E P(t/A) P lExP (A/E)+ PlE) xP(A/E) 3 3 X 6+ 46 22 f (E,/A) Gikaly accidant is the moYe Tha Cal in One haue hean lue Lo