Bayes' Theorem

Q. A man is known to speak truth 2 out of 3 times. He throws a die and reports that number obtained is a four. Find the probability that the number obtained is actually a four.

1. $\frac{2}{7}$
2. $\frac{3}{7}$
3. $\frac{4}{7}$
4. $\frac{3}{4}$

Q. A man speaks 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.

1. $\frac{3}{8}$
2. $\frac{5}{8}$
3. $\frac{7}{8}$
4. $\frac{1}{12}$

Q. 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 $\frac{1}{3}$ and the probability that he copies the answer is $\frac{1}{6}$. The probability that his answer is correct, given that he copies it, is $\frac{1}{8}$. Find the probability that he knows the answer to the question, given that he correctly answered it.

1. $\frac{17}{39}$
2. $\frac{13}{29}$
3. $\frac{24}{29}$
4. $\frac{24}{39}$

Q. A card from a pack of 52 cards is lost. From the remaining cards of pack, two cards are drawn and are found to be diamonds. Find the probability of the missing card to be a diamond.

1. $\frac{23}{25}$
2. $\frac{3}{26}$
3. $\frac{39}{50}$
4. $\frac{11}{50}$

Q. In a toy-making factory, machines A, B and C manufacture 25%, 35% and 40% of the total toys respectively. Of their output, 5% 4% and 2% respectively are defective toys. A toy is drawn at random from the product. If the toy drawn is found to be defective, what is the probability that it is manufactured by the machine B?

1. $\frac{17}{69}$
2. None of these
3. $\frac{28}{69}$
4. $\frac{35}{69}$

Q. There are 3 boxes each containing 3 red and 5 green balls. Also, there are 2 boxes each containing 4 red and 2 green balls. A green ball is selected at random. Find the probability that this green ball is from a box of the first group.

1. $\frac{54}{61}$
2. $\frac{45}{61}$
3. $\frac{8}{31}$
4. None of these

Q. An architecture company built 200 bridges, 400 hospitals and 600 hotels. The probabilities of damage due to an earthquake to a bridge, hospital and hotel are 0.01, 0.03 and 0.15 respectively. One of the construction gets damaged by the earthquake. What is the probability that it is a bridge?

1. $\frac{1}{26}$
2. $\frac{1}{52}$
3. $\frac{7}{52}$
4. $noneofthese$

Q. Three boxes contain 6 red, 4 black; 5 red, 5 black and 4 red, 6 black balls respectively. One of the box is selected at random and a ball is drawn from it. If the ball drawn is red, then the probability that it is drawn from the first bag is k. The value of 10k is___.

Q. An architecture company built 200 bridges 400 hospitals and 600 hotels. The probability of damage due to earthquake of a bridge. hospital and hotel is 0.01, 0.03 and 0.15 respectively. One of the construction gets damaged with earthquake. What is the probability that is a bridge?

1. $noneofthese$
2. $\frac{1}{26}$
3. $\frac{1}{52}$
4. $\frac{7}{52}$

Q. A man speaks 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.

1. $\frac{3}{8}$
2. $\frac{5}{8}$
3. $\frac{7}{8}$
4. $\frac{1}{12}$