A die is thrown 10 times. The probability that an odd number will come up at least once is

A random variable $X$ has the following probability distribution:

If the mean of the random variable $X$ is $1 / 3$, then the variance is

If a random variable $X$ follows the binomial distribution with parameters $n=5, p$ and $P(X=2)=9 P(X=3)$, then $p$ is equal to

A bag contains $$2 n+1$$ coins. It is known that $$n$$ of these coins have head on both sides whereas, the other $$n+1$$ coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is $$\frac{31}{42}$$, then the value of $$n$$ is