A random variable X has the following probability distribution:

$X=x_i$	1	2	3	4
$P(X=x_i)$	k	2k	3k	4k

The value of $P(X\ge 3)$ is

A couple has 3 children each child is equally likely to be a boy or a girl. The probability that the eldest child is a girl given that they have atleast one boy is:

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:

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 of the person to be tested as COVID positive, given that he is actually not having COVID is :

The probabilities of occurrence of two events E and F are 0.25 and 0.50 respectively. The probability of their simultaneous occurrence is 0.14. The probability that neither E nor F occurs is

If A and B are two independent events such that P(A) = 1/3, $P(A\cup B) = 3/5$ and P(B) = p, then which of the following are true?

(A) The value of p is $\frac{2}{5}$

(B) $P(A\cap B) = \frac{2}{15}$

(C) $P(B/A) = \frac{1}{3}$

(D) $P(A/B) = \frac{3}{5}$

Choose the correct answer from the options given below:

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