Person $A$ can solve $90 \%$ of the problems given in the book and Person $B$ can solve $70 \%$. Then,the probability that at least one of them will solve the problem selected at random from the book is

One die of red colour,one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled,its colour and the number on its uppermost face is noted. Describe the sample space.

In a simultaneous throw of a pair of dice,the probability of getting a total more than $7$ is

The probability of solving a problem by three persons $A, B$ and $C$ independently is $\frac{1}{2}, \frac{1}{4}$ and $\frac{1}{3}$ respectively. Then the probability that the problem is solved by exactly two of them is

$A$ coin is tossed twice. What is the probability that at least one tail occurs?

$A, B, C$ are aiming to shoot a balloon. $A$ will succeed $4$ times out of $6$ attempts. The chance of $B$ to shoot the balloon is $3$ out of $5$ and that of $C$ is $2$ out of $3$. If the three aim to shoot the balloon simultaneously, then the probability that at least two of them hit the balloon is