India and Pakistan play a $5$-test hockey series. What is the probability that India wins at least three games?

The probability of a man hitting a target is $\frac{1}{10}$. The least number of shots required,so that the probability of his hitting the target at least once is greater than $\frac{1}{4}$,is

$A$ fair coin is tossed $100$ times. The probability of getting tails an odd number of times is

$A$ binary number is made up of $16$ bits. The probability of an incorrect bit appearing is $p$ and the errors in different bits are independent of one another. The probability of forming an incorrect number is

In a multiple-choice examination, there are $10$ questions with one correct option out of $4$ options for each question. $A$ student gets $4$ marks for each correct answer and $1$ mark is deducted for each incorrect answer. The probability that a student, guessing randomly on every question, scores $30$ marks in this exam is... (in $/4^{10}$)

If $7$ different balls are distributed among $4$ different boxes,then the probability that the first box contains $3$ balls is