$A$ coin is tossed $3$ times. The probability of getting exactly two heads is

$A$ speaks truth in $20 \%$ of the cases and $B$ in $80 \%$ of the cases. Find the probability that their statements about an incident do not match.

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 $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5}$, $P(\bar{A} \cup \bar{B}) = \frac{7}{10}$, and $P(B) = \frac{2}{5}$, then $P(A)$ equals

Let $S$ be the set of all quadratic equations of the form $x^2+bx+c=0$,where $b, c \in \{1, 2, 3, 4, 5, 6\}$. If an equation is selected at random from $S$,then the probability that the equation has real roots is

$A$ die is thrown. Find the probability of the following event: $A$ number greater than or equal to $3$ will appear.