Answer to Question #210787 in Statistics and Probability for Farah

Question

A consulting firm rent cars from two agencies, 45% from agency P and 55% from agency Q. It is known that 8% of the cars from agency P and 6% of the cars from agency Q have bad tyres.

Draw a tree diagram for the above situation.

ii) Find the firm will get a car with bad tyres.

iii) If a car rented by the firms has good tyres, find the probability that it came from agency Q.

Answer 1

Tree diagram.

i. $P(Bad)$

$P(Bad)=P(P\cap Bad)+ P(Q\cap Bad)$

$=(0.45\times0.08)+(0.55\times0.06)$

$=0.036+0.033=0.069$

P(Bad)= 0.069

ii. $P(Q|Good)$

$P(Q|Good)=\frac{P(Q\cap Good)}{P(Good)}$

$P(Q|Good)=\frac{P(Q\cap Good}{1-P(Bad)}$

$=\frac{0.55\times0.06}{1-0.069}=0.03545$

P(Q|Good)=0.03545