Two balls are drawn at random from a bag containing 5 black balls and 3 white balls. If the random variable $X$ denotes the number of white balls drawn, then the mean of $X$ is

If the mean and variance of a binomial distribution are 4 and $\frac{4}{3}$ respectively, then $P(X=2)=$

If a man throws a die until he gets a number bigger than 3 , then the probability that he gets a 5 in his last throw is

A diagnostic test has the probability 0.95 of giving a positive result when applied to a person suffering from a certain disease and a probability 0.10 of giving a positive result when given to a non-sufferer. It is estimated that $0.5 \%$ of the population are suffering from the disease. If this test is now administered to a person from this population about whom there is no information relating to the incidence of this disease and the test gives a positive result, then the probability that he is a sufferer, is