Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

Two dice are rolled. If both dice have six faces numbered $1, 2, 3, 5, 7, 11$,then the probability that the sum of the numbers on the uppermost faces is a prime number is:

If $A, B$ and $C$ are three events of a random experiment with $P(A)=0.4, P(B)=0.3$ and $P(A \cap B)=0.2$,then the probability that neither $A$ nor $B$ occurs is

There are $5$ horses in a race. Mr. $A$ selects $2$ horses at random and bets on them. What is the probability that the winning horse is among the horses selected by Mr. $A$ (in $/5$)?

$A$ rational number is selected at random from the distinct rational numbers of the form $p/q$ formed with $p$ and $q$ belonging to the set $\{1, 2, 3, 4, 5, 6\}$. The probability that the rational number selected is a proper fraction is:

Three students $X, Y$ and $Z$ appear for an examination. The probability of $X$ passing the examination is $\frac{1}{5}$,the probability of $Y$ passing the examination is $\frac{1}{4}$ and the probability of $Z$ failing the examination is $\frac{2}{3}$. The probability that at least two of them pass the exam is