A person is known to speak the truth in 3 out of 4 occasions. If he throws a die and reports that it is six, then the probability that it actually six is

$70 \%$ of the total employees of a factory are men. Among the employees of that factory 30\% of men and $15 \%$ of women are technical assistants. If an employee chosen at random is found to be a technical assistant, then the probability that this employee is a man is

If a discrete random variable $X$ has the probability distribution $P(X=x)=k \frac{2^{2 x+1}}{(2 x+1)!}, x=0,1,2 \ldots \infty$, then $k=$

A random variable $X$ follows a binomial distribution in which the difference between its mean and variance is 1. if $2 P(x=2)=3 P(x=1)$, then $n^2 P(x>1)=$