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:

A bag contains 6 red balls, 4 green balls and 10 blue balls. Three balls are drawn with replacement. The probability of getting at least 1 green ball is:

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X denotes the number of Spades in two draws, then

Match the LIST-I with LIST-II

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 :

Probability that a man speaks truth is $\frac{3}{4}$. He throws a die and reports that it is a six. The probability that it is actually a six is

A doctor is to visit a patient. It is known that the probabilities that he will come by train, bus, scooter or by other means of transport are respectively $\frac{3}{10}, \frac{1}{5}, \frac{1}{10}$ and $\frac{2}{5}$. The probabilities that he will be late are $\frac{1}{4}, \frac{1}{3}$ and $\frac{1}{12}$, if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he arrives late.

The probability that he comes by bus is:

In a box containing 100 bulbs, 10 are defective. Then the probability, that out of a sample of 5 bulbs none is defective, is: