During the winter months,in a certain village in Scotland,the probability of a day having severe fog is $0.6$. The probability that in a given week there will be exactly two days with severe fog is:

If the mean and the variance of a Binomial variate $X$ are $2$ and $1$ respectively,then the probability that $X$ takes a value greater than or equal to $1$ is

If the mean and the variance of a Binomial variate $X$ are $2$ and $1$ respectively,then the probability that $X$ takes a value greater than $1$ is equal to

$A$ box contains $30$ toys of the same size,in which $10$ toys are white and the remaining toys are blue. $A$ toy is drawn at random from the box and it is replaced in the box after noting down its colour. If $5$ toys are drawn in this way,then the probability of getting at most $2$ white toys is

In a binomial distribution,the mean is $15$ and the variance is $10$. Then the parameter $n$ is:

Suppose $X$ has a binomial distribution $B(6, 1/2)$. Show that $X=3$ is the most likely outcome.
(Hint: $P(X=3)$ is the maximum among all $P(x_i)$,where $x_i = 0, 1, 2, 3, 4, 5, 6$)