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
$\frac{2}{3}$
$\frac{4}{3}$
$\frac{1}{3}$
$1$
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 : $A$ and $C$ are mutually exclusive
Two dice are tossed. The probability that the total score is a prime number is
An integer is chosen at random and squared. The probability that the last digit of the square is $1$ or $5$ is
A card is drawn at random from a pack of $52$ cards. The probability that the drawn card is a court card i.e. a jack, a queen or a king, is
Three coins are tossed once. Find the probability of getting exactly $2$ tails.