question

an insurance company insured 3000 cyclists, 6000 scooter drivers and 9000 car drivers. the probability of an accident involving a cyclist, a scooter driver and a car driver are 0·3, 0·05 and 0·02 respectively. one of the insured persons meets with an accident. what is the probability that he is a cyclist ?

 

 

 

 

 

 

 

 

let the events are defined as e1: the person chosen is a cyclist.
e2: person chosen is a scooter driver.
e3:person chosen is a car driver and
a: the person meets with an accident.
then

also,

thus required probability,