Q7 of 105 Page 555

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively.

One of the insured persons meets with an accident. What is the probability that he is a scooter driver?

Given: let E1 be the event that the driver is a scooter driver, E2 be the event that the driver is a car driver and E3 be the event that the driver is a truck driver. Let A be the event that the person meet with an accident.

Total number of drivers = 2000 + 4000 + 6000 = 12000


Then


And


And


As we a headed coin has head on both sides so it will shows head.


Also P(A|E1) = P (accident of a scooter driver)


And P(A|E2) = P (accident of a car driver)


And P(A|E3) = P (accident of a truck driver)


Now the probability that the driver is a scooter driver, being given that he met with an accident, is P(E1|A).


By using bayes’ theorem, we have:







More from this chapter

All 105 →
5

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?

 6

There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin?

 8

A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B?

 9

Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.