Dependent Events

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

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

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. Dependent events, 5

1. 2
2. 1
3. 3
4. 4

Q. Dependent events, 3

1. 1
2. 3
3. 4
4. 2

Q. Dependent events, 1

1. 2
2. 3
3. 4
4. 1

Q. A bag contains 3 red, 6 white and 7 blue balls. Two balls are drawn one by one. What is the probability that first ball is white and second ball is blue where first drawn ball is not replaced in the bag?

1. $\frac{7}{40}$
2. $\frac{9}{40}$
   
3. $\frac{11}{40}$
   
4. $\frac{3}{40}$
   

Q. A bag contains 4 red and 4 blue balls. Four balls are drawn one by one from the bag, then find the probability that the drawn balls are in alternate colour.

1. $\frac{6}{31}$
   
2. $\frac{8}{35}$
   
3. $\frac{6}{35}$
4. $\frac{8}{31}$
   

Q. A bag contains 3 red and 7 black balls, two balls are taken out at random without replacement. If the first ball taken out is red, then the probability that the second taken out ball is red:

1. $\frac{2}{21}$
2. $\frac{1}{10}$
3. $\frac{1}{15}$
4. $\frac{3}{10}$

Q. A box contains 3 white and 2 red balls. If the first drawn ball was not replaced then the probability that the second drawing ball will be red is

1. $\frac{8}{25}$
2. $\frac{3}{5}$
3. $\frac{2}{5}$
4. $\frac{21}{35}$