Let $S$ be the sample space of a random experiment and $P$ be a probability function defined on the power set of $S$. Two events $A$ and $B$ of the random experiment are called independent if

If three boxes contain $3$ white and $1$ black,$2$ white and $2$ black,and $1$ white and $3$ black balls respectively,and one ball is chosen at random from each box,what is the probability of selecting $2$ white and $1$ black ball?

Cards are drawn one after the other without replacement from a well-shuffled pack of cards until an ace card appears. If the probability that exactly $5$ cards are drawn before the first ace card appears is $\frac{4}{49}\left(\frac{p_1 \cdot p_2 \cdot p_3}{p_4 \cdot p_5 \cdot p_6}\right)$, where $p_i$ is prime for $i=1, 2, 3, 4, 5, 6$, then $(\max \{p_i\} - \min \{p_i\}) = $

Let the mean and variance of $7$ observations $2, 4, 10, x, 12, 14, y$ (where $x > y$) be $8$ and $16$ respectively. Two numbers are chosen from the set $\{1, 2, 3, x-4, y, 5\}$ one after another without replacement. Then the probability that the smaller number among the two chosen numbers is less than $4$ is:

$A$ coin is tossed $2020$ times. The probability of getting head on $1947^{\text{th}}$ toss is

$P$ speaks truth in $70\%$ of the cases and $Q$ in $80\%$ of the cases. In what percent of cases are they likely to agree in stating the same fact (in $\%$)?