A coin is tossed 7 times. The probability of getting at least 4 heads 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 of the person tested as COVID positive, given that he is actually having COVID is :

If a fair coin is tossed 10 times, then the probability of obtaining at least one head is :

A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A is

If E and F are two events such that $P(E \cup F)=P(E)$, then

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:

Probabilities to solve a specific problem by A, B and C are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. Probability that at least one will solve the problem is: