$A$ die is thrown $5$ times. Getting an odd number is considered a success. Find the variance of the distribution of successes.

Let $X$ be the number of successes in $n$ independent Bernoulli trials with probability of success $p = \frac{3}{4}$. The least value of $n$ so that $P(X \ge 1) \ge 0.9375$ is . . . . . .

If $X \sim B(n, p)$ then $\frac{P(X=k)}{P(X=k-1)}=$

$A$ person tossing a biased coin indefinitely wins the game by getting head for the first time. The probability that he wins the game in an odd number of tosses is $3/4$. If $5$ such coins are tossed at a time, then the probability that head appears on all the coins is:

$A$ die is tossed twice. Getting a number greater than $4$ is considered a success. Then the variance of the probability distribution of the number of successes is

$A$ bag contains $4$ red and $3$ black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let $X$ denote the number of times a black ball is drawn in $3$ draws. Assuming that at each draw each ball is equally likely to be selected,then the probability distribution of $X$ is given by: