BAY'S THEOREM

          BAYE'S THEOREM

1) In a bolt factory, machines A,B,C manufacture 25%,35%,40% of the total bolts. Of their output 5,4 and 2% are defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found to be defective, what is the probability that it is manufactured by the machine B?      28/69

2) Three Urns contains 6 red 4 black; 4 red, 6 black, and 5 red and 5 black balls. One of the urns is selected at random and a ball is drawn from it. If the ball drawn is red, find the probability that is drawn from the first urn.          2/5

3) There are 3 bags, each containing 5 white and 3 black balls. Also there are 2 bags, each containing 2 white and 4 black balls. A white ball is drawn at random. Find the probability that this white ball is from a bag of the first group. 45/61

4) A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.   

                                                 3/8

5) In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is 1/3 and the probability that he copies the answer is 1/6. The probability that his answer is correct, given that he copied it, is 1/8. Find the probability that he knew the answer to the question, given that he correctly answered it.

                     24/29

6) A card from a pack of 52 Cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be hearts. Find the probability of the missing card to be a heart.     11/50

7) A letter is known to have come either from TATANAGAR or CALCUTTA. On the envelope just two consecutive letters TA are visible. What is the probability that the letter has come from

A) Calcutta.          4/11

B) Tatanagar.        7/11