Question

An insurance company insured 2000 scooters and 3000 motor cycles. The probability of an accident involving a scooter is 0.01 and that of a motor cycle is 0.02. An insured vehicle met with an accident. Find the probability that the accidented vehicle was a motor cycle.

Answer 1

$\begin{array}{c}P\left(E_1\right)=\frac{2000}{5000}=0.4\\ P\left(E_2\right)=\frac{3000}{5000}=0.6\\ P\left(\frac{A}{E_1}\right)=0.01\\ P\left(\frac{A}{E_2}\right)=0.02\\ P\left(\frac{E_2}{A}\right)=\frac{P\left(E_1\right)P\left(\frac{A}{E_2}\right)}{\begin{array}{c}P\left(E_1\right)P\left(\frac{A}{E_1}\right)+P\left(E_2\right)P\left(\frac{A}{E_2}\right)\\ =\frac{0.6\times 0.02}{0.6\times 0.02+0.4\times 0.01}\\ =\frac{0.012}{0.012+0.004}\\ =\frac{3}{4}\end{array}}\end{array}$