If getting a head on a coin when it is tossed is considered as success, then the probability of having more number of failures when ten fair coins are tossed simultaneously is

Five cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. What is the probability that all the five cards are spades?

$A$ fair coin is tossed $n$ times. If the probability that head occurs $6$ times is equal to the probability that head occurs $8$ times,then $n$ is equal to:

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

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:

$A$ fair coin is tossed $9$ times. On each toss, a man predicts that the outcome will be heads. The probability that the number of successful predictions is strictly greater than the number of unsuccessful predictions is...