The probabilities of winning the race by two athletes $A$ and $B$ are $\frac{1}{5}$ and $\frac{1}{4}.$ The probability of winning by neither of them, is
$\frac{3}{5}$
$\frac{3}{4}$
$\frac{2}{5}$
$\frac{4}{5}$
The probabilities of a problem being solved by two students are $\frac{1}{2},\frac{1}{3}$. Then the probability of the problem being solved is
The probability of happening of an impossible event i.e. $P\,(\phi )$ is
A determinant is chosen at random. The set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that value of the determinant chosen is positive, is
A coin is tossed. If the out come is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?
A pair of a dice thrown, if $5$ appears on at least one of the dice, then the probability that the sum is $10$ or greater is