A farmer has a tubewell which works by connecting two switches $S_1$ and $S_2$. The probability that $S_1$ works is 9/10 and the probability that $S_2$ works is 8/10. The farmer connects them in series in 30% cases and in parallel in 70% cases. If it is known that the tubewell was working, what is the probability that it was a series connection.

Match List-I with List-II

Let A & B are two events such that P(A)=0.8, P(B)=0.5, P(B|A)=0.4

Choose the correct answer from the options given below:

A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than 9, given that the black resulted in a 5 is

Urn I contains 6 red balls and 4 black balls and Urn II contains 4 red balls and 6 black balls. One ball is drawn at random from Urn I and placed in Urn II. If one ball is drawn at random from Urn II, then the probability that it is a red ball is :

The probability that the study time of students is exactly 2 hours

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 :

A letter is known to have come either from LONDON or CLIFTON. On the envelop just two consecutive letter 'ON' are visible. The probability that the letter has come from LONDON is: