A coin is tossed K times. If the probability of getting $3$ heads is equal to the probability of getting $7$ heads, then the probability of getting $8$ tails is :

Probabilities of solving a specific mathematical problem independently by three students are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$. If all the three students try to solve the problem independently, the probability that the problem is solved, is:

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. Then variance of the number of kings is

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

A player participates in 3 matches against three teams T₁, T₂ and T₃.The probability of winning a match against teams T₁, T₂ and T₃ are 0.2, 0.3 and 0.9 respectively. If 'wins' can be regarded as independent events, then the probability that he

(A) wins all the 3 matches is 0.054

(B) wins no match is 0.054

(C) wins exactly two matches is 0.348

(D) wins exactly one match is 0.542

Choose the correct answer from the options given below:

If X is a normal variate with mean 16 and standard deviation 4, then the value of standard normal variate Z corresponding to X = 17 is: