Among every $8$ units of a product, one is likely to be defective. If a consumer has ordered $5$ units of that product, then the probability that at most one unit is defective among them is

On an average, nine out of $10$ ships that have departed at $A$ reach $B$ safely. The probability that out of five ships that have departed at $A$, at least four will reach $B$ safely is

Suppose $X$ follows a binomial distribution with parameters $n$ and $p$,where $0 < p < 1.$ If $\frac{P(X = r)}{P(X = n - r)}$ is independent of $n$ and $r$,then

$A$ contest consists of predicting the results (win,draw,or defeat) of $7$ football matches. $A$ sent his entry by predicting at random. The probability that his entry will contain exactly $4$ correct predictions is:

Suppose a machine produces metal parts that contain some defective parts with probability $0.05$. How many parts should be produced in order that the probability of at least one part being defective is at least $1/2$? (Given that, $\log_{10} 95 = 1.977$ and $\log_{10} 2 = 0.3$)

If the mean and variance of a binomial variate $X$ are $8$ and $4$ respectively,then $P(X < 3)$ equals to