$A$ fair coin is tossed $15$ times. The probability that the tail will appear at least thrice is

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X \sim B(n_1, 0.5)$ and $Y \sim B(n_2, 0.4)$. If the variance of both $X$ and $Y$ is $6$,then $\sqrt{n_1+n_2}=$

The probability of getting a success in a trial is five times that of a failure. The probability of getting at most one success in $5$ trials is:

If a random variable $X$ follows the Binomial distribution $B(10, p)$ such that $5 P(X=0) = P(X=1)$,then the value of $\frac{P(X=5)}{P(X=6)}$ is equal to

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 a Bernoulli trial is conducted $n$ times,then which one of the following is not suitable to use Poisson distribution?
$(i)$ Each trial results in two mutually exclusive outcomes namely success,failure.
(ii) The number $n$ of such trials is sufficiently large.
(iii) The trials are independent of each other.
(iv) The probability $p$ of success in each trial is very large.