Answer to Question #192991 in Statistics and Probability for sagun poudel

Question

An insurance company insured 1000 scooter drivers, 3000 car drivers and 6000 truck drivers. The

probabilities that the scooter, car and truck drivers meet with an accident are 0.2, 0.04 and meets

with an accident. What is the probability that he is a car drivers ?

Answer 1

Let, A denote scoter drivers $\Rightarrow P(A)=\dfrac{1000}{10000}=0.1$

B denote car drivers $\Rightarrow P(B)=\dfrac{3000}{10000}=0.3$

C denote truck drivers $\Rightarrow P(C)=\dfrac{6000}{10000}=0.6$

Let M denote the event that the driver meet an accident.

Probability that scooter driver meet accident P(M/A)=0.2

Probability that car driver meet accident P(M/B)=0.04

Probability that truck driver meet accident P(M/C)=0.13

probability that driver meets an accident and he is a car driver-

$P(A/M)=\dfrac{P(A)*P(M/A)}{P(A)*P(M/A)+P(B)*P(M/B)+P(C)*P(M/C)}$

$=\dfrac{0.1(0.2)}{0.1(0.2)+0.3(0.04)+0.6(0.13)}\\[9pt] =\dfrac{0.02}{0.02+0.012+0.78}=\dfrac{0.02}{0.812}=0.02463$