$A$ bag contains $5$ black balls,$4$ white balls and $3$ red balls. If a ball is selected at random,the probability that it is a black or a red ball,is

Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. If all hit at the target independently,then the probability that the target would be hit,is

The vertices of a regular tetrahedron are marked $1, 2, 3, 4$. If three such tetrahedra are thrown simultaneously,what is the probability that the sum of the numbers on the faces is $5$?

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up $4$,$E_2$ is the event that die $B$ shows up $2$,and $E_3$ is the event that the sum of numbers on both dice is odd,then which of the following statements is $NOT$ true?

$A$ six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once 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