The probability of not getting $53$ Tuesdays in a leap year is :

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

Based on the above informations, answer the question :

The probability that the person is actually having COVID given that he is tested as COVID positive is :

The probability of drawing a one-hundred rupee currency from two boxes one of which contain 3 fifty-rupee currency and 2 one-hundred rupee and other box contain 2 fifty-rupee currency and 3 one-hundred rupee currency notes is-

If A and B are two events such that $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$, then which of the following statements are true?

(A) A and B are independent events

(B) $P(A | B) = \frac{3}{4}$

(C) $P(A' | B') = \frac{5}{8}$

(D) $P(A' | B) = \frac{1}{4}$

Choose the correct answer from the options given below:

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

(A) $\bar{A}$ and B are independent events

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

(C) $\bar{A}$ and $\bar{B}$ are independent events

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

Choose the correct answer from the options given below:

If the random variable X is normally distributed with mean 16 and standard deviation 4, then the standard normal variable Z corresponding to X = 17 is

The mean of the number of heads in a simultaneous toss of three coins is