Question

An insurance company provided insurance cover to 3000 trucks, 5000 buses and
4000 cars. The probabilities of their getting involved in an accident are 0.1, 0.2
and 0.4 respectively. If an accident is reported, what is the probability that it
involves the truc

Answer 1

Answer:

0.1/3000 is the answer

Answer 2

Answer:

If an accident is reported, what is the probability that it involves the truck is $=\frac{3}{29}$.

Given:

An insurance company provided insurance cover to 3000 trucks, 5000 buses and  4000 cars.

The probabilities of their getting involved in an accident are 0.1, 0.2  and 0.4 respectively.  

To find:

If an accident is reported, what is the probability that it involves the truck

Solution:

$A_{1}$ be the event that the truck is insured

$p(A_{1}) = \frac{3000}{(3000 + 5000 + 4000)} = \frac{1}{4}$

$A_{2}$ be the event that the bus is insured

$p(A_{2}) = \frac{5000}{(3000+ 5000 + 4000)} = \frac{5}{12}$

$A_{3}$ be the event that the car is insured

$p(A_{3}) = \frac{4000}{(3000 + 5000 + 4000)} = \frac{1}{3}$

Probability of truck in an accident = 0.1 =$\frac{1}{10}$

Probability of bus in an accident = 0.2 = $\frac{2}{10}$

Probability of car in an accident = 0.4 =$\frac{4}{10}$

Probability of truck getting an accident  $=\frac{\left(\frac{1}{4} \times \frac{1}{10}\right)}{\left(\frac{1}{4} \times \frac{1}{10}\right)}+\left(\frac{5}{12} \times \frac{2}{10}\right)+\left(\frac{1}{3} \times \frac{4}{10}\right)$

$=\frac{\frac{1}{40}}{\frac{1}{40}}+\left(\frac{1}{12}\right)+\left(\frac{2}{15})\right)$

$=\frac{\frac{1}{40}}{\frac{29}{120}}$

$=\frac{3}{29}$

Result:

If an accident is reported, what is the probability that it involves the truck  is $=\frac{3}{29}$.