Q6 of 105 Page 555

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?

Given: let E1 be the event of choosing a two headed coin, E2 be the event of choosing a biased coin and E3 be the event of choosing an unbiased coin. Let A be the event that the coin shows head.

Then P (E1) = P (E2) = P (E3) = 1/3


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


Also P(A|E1) = P (correct answer given that he knows) = 1


And P(A|E2) = P (coin shows head given that the coin is biased)


And P(A|E3) = P (coin shows head given that the coin is unbiased)


Now the probability that the coin is two headed, being given that it shows head, is P(E1|A).


By using bayes’ theorem, we have:







More from this chapter

All 105 →
4

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4. What is the probability that the student knows the answer given that he answered it correctly?

 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?

 7

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?

 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?