In a box containing $100$ bulbs,$10$ are defective. The probability that out of $20$ bulbs selected at random,none is defective is

It is observed that $25 \%$ of the cases related to child labour reported to the police station are solved. If $6$ new cases are reported,then the probability that at least $5$ of them will be solved is

If $X$ follows the Binomial distribution with parameters $n=6$ and $p$ and $9 P(X=4) = P(X=2)$,then $p$ 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:

$A$ box has $100$ pens of which $10$ are defective. The probability that out of a sample of $5$ pens drawn one by one with replacement,at most one is defective is:

Ten eggs are drawn successively with replacement from a lot containing $10 \%$ defective eggs. Find the probability that there is at least one defective egg.