Three urns contain 6 red, 4 black; 4 red, 6 black and 5 red, 5 black marbles respectively. One of the urns is selected at random and a marble is drawn from it. If the marble drawn is red, then the probability that it is drawn from the first urn is

A company manufactured fans with three units A, B and C. Unit A, B and C produces 2%, 10% and 14% defective fans respectively. Units A, B and C produces 40%, 40% and 20% fans of total products respectively. A fan is randomly chosen that is found to be defective then the probability that the chosen fan is produced from unit C, is

The probability of a shooter of hitting the target is $\frac{1}{4}$. The minimum number of fire needed so that the probability of hitting the target atleast once is greater than $\frac{7}{16}$ is:

Two numbers are selected at random from the integers 1 through 19. If the sum is even, then the probability that both are odd numbers is:

If A and B are independent events, then which of the following is not true?

Two thirds of the students in a class are boys and the rest are girls. It is known that the probability of a girl getting a first class is 0.25 and that of a boy getting a first class is 0.28, then the probability that a student chosen at random will get first class marks in the subject is

If A and B are two events such that $A \neq \emptyset$, B $\neq \emptyset$, then which of following is/are TRUE:

A. $P(B/A)=P(A).P(B)$

B. $P(B/A)=\frac{P(A\cap B)}{P(A)}$

C. $P(A'/B')=\frac{1-P(A\cup B)}{1-P(B)}$

D. $P(B/A).P(A/B)=2$

Choose the correct answer from the options given below: