Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$. Then the probability that the problem is solved correctly by at least one of them is

Out of $100$ students, two sections of $40$ and $60$ are formed. If you and your friend are among the $100$ students, what is the probability that you both enter the same section ?

Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $\frac{ k }{2^{15}}$, then $k$ is equal to:

From a well shuffled pack of $52$ playing cards, cards are drawn one by one with replacement. Probability that $5^{th}$ card will be "king of hearts" is

Find the probability that when a hand of $7$ cards is drawn from a well shuffled deck of $52$ cards, it contains atleast $3$ Kings.

A man draws a card from a pack of $52$ playing cards, replaces it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two times is