A four digit number is formed by using the digits 1, 2, 4 and 5 with no repetition. The probability that the number is divisible by 5, is

During a season change, a pathologist observed that out of 10,000 people tested for viral fever, 1000 people were tested positive. Then the standard deviation for the distribution of positive reports is_______

Let box I contains 3 black and 4 white balls, box II contains 2 black and 2 white balls, box III contains 4 black and 3 white balls. A box is selected at random and then a ball is randomly drawn from the selected box. If the color of the ball is black then the probability that the ball is drawn from box III, is:

If A and B are two independent events, then which of the following is/are true?

(A) $P(A \cap B) = 0$

(B) $P(A \cup B) = 1 - P(A')P(B')$

(C) $P(A \cup B) = P(A)P(B)$

(D) $P(A \cap B) = P(A)P(B)$

Choose the correct answer from the options given below:

If $P(A) = \dfrac{3}{10}, P(B) = \dfrac{3}{4}$ and $P(A\cap B) = \dfrac{1}{5}$, then $P(B\mid A)$ is equal to:

The binomial distribution for which the mean is 5 and variance 4, is

The probability that in a year of the 22nd century choosen at random, there will be 53 Sundays is: