The probability of $A, B, C$ solving a problem are $\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is
$\frac{{25}}{{168}}$
$\frac{{25}}{{56}}$
$\frac{{20}}{{168}}$
$\frac{{30}}{{168}}$
Two coins are tossed. Let $A$ be the event that the first coin shows head and $B$ be the event that the second coin shows a tail. Two events $A$ and $B$ are
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.
A card is selected from a pack of $52$ cards. Calculate the probability that the card is black card.
Two dice are thrown. The events $A,\, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$
State true or false $:$ (give reason for your answer)
Statement : $A=B^{\prime}$
The sum of two positive numbers is $100$. The probability that their product is greater than $1000$ is