If $X \sim B(35, p)$ such that $7 P(X=0)=P(X=1)$,then the value of $\frac{P(X=15)}{P(X=20)}$ is equal to

It is observed that there will be $25$ blood specimens of normal persons,if $100$ blood samples are tested. If $10$ specimens are sent to a laboratory for testing,then the probability of having at least two specimens of normal persons is

Let $C_1$ and $C_2$ be two biased coins such that the probabilities of getting a head in a single toss are $\frac{2}{3}$ and $\frac{1}{3}$,respectively. Suppose $\alpha$ is the number of heads that appear when $C_1$ is tossed twice,independently,and $\beta$ is the number of heads that appear when $C_2$ is tossed twice,independently. Then,the probability that the roots of the quadratic polynomial $x^2 - \alpha x + \beta$ are real and equal is:

$A$ radar system can detect an enemy plane in one out of $10$ consecutive scans. The probability that it cannot detect an enemy plane at least two times in four consecutive scans is:

$A$ die is thrown $100$ times. If the success is defined as getting an even number,then the variance of the number of successes is:

Let a biased coin be tossed $5$ times. If the probability of getting $4$ heads is equal to the probability of getting $5$ heads,then the probability of getting at most two heads is