Let $A$ and $B$ be two events such that $P(A \cap B) = \frac{1}{6}$,$P(A \cup B) = \frac{31}{45}$,and $P(\bar{B}) = \frac{7}{10}$. Then which of the following is true?

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that one of them is black and the other is red.

In a single throw of three dice,the probability of getting a sum at least $5$ is

Consider the system of equations $ax+by=0, cx+dy=0$,where $a, b, c, d \in \{0, 1\}$.
$STATEMENT-1$: The probability that the system of equations has a unique solution is $3/8$.
$STATEMENT-2$: The probability that the system of equations has a solution is $1$.

Let $0 < P(A) < 1$,$0 < P(B) < 1$ and $P(A \cup B) = P(A) + P(B) - P(A)P(B).$ Then

You are given a box containing $20$ cards. Out of these,$10$ cards have the letter $I$ printed on them,and the other $10$ cards have the letter $T$ printed on them. If you draw three cards one after another with replacement,what is the probability of forming the word $IIT$?