Eight person stand in a line at random. What is the probability that two person X and Y don't stand together.

If 8 person are to sit around a table what is the probability that X and Y don't sit together

Suppose 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? (Assume that these are equal number of males and females)

Five boys and four girls randomly stand in a line. Find the probability that no two girls come together.

Five boys and four girls randomly stand in a line. Find the probability that no two girls come together.

There are three coins. One is a two tailed coin (having tail on both faces) another is a biased coin that comes up heads 60% of the times and third is an unbiased coln. One of the three coins is chosen at random and tossed and it shows tail. What is the probability that it is a two tailed coin.

A laboratory blood test is 99% effective in detecting a certain disease,when it is infact present. However, the test also yields a false positive result for 0.5% of the healthy person tested (ie. if a healthy person is tested, then with probability 0.005, the test will imply he has the disease). If 0.1% of the population actually has the disease, then what is the probability that a person has disease, given that his test result is positive?

By examining the chest X-ray, the probability that TB is detected when a person is actually suffering is 0.99. The probability of an healthy person diagnosed to have TB is 0.001. In à certain city, 1 in 1000 people suffers from TB. A person is selected at random and is diagnosed to have TB. What is the probability that he actually has TB?

A person buys a lottery ticket in 50 lotteries in each of which his chance of winning a prize is 1/100. What is the probability that he will win a prize atleast once?

A person buys a lottery ticket in 50 lotteries in each of which his chance of winning a prize is 1/100. What is the probability that he will win a prize atleast twice?