If $A$ and $B$ are two events,then which of the following is $NOT$ true?

If $A$ and $B$ are two events of a random experiment such that $P(\bar{A})=\frac{2}{3}$,$P(B)=\frac{4}{15}$ and $P(A \cap \bar{B})=\frac{1}{5}$,then $\sqrt{195[P(B \mid(A \cup \bar{B}))+P(A \cup B)]} = $

$A$ and $B$ are two independent events of a random experiment and $P(A) > P(B)$. If the probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occurs is $\frac{1}{3}$,then the probability of the occurrence of $B$ is

In a battery manufacturing factory,machines $P$,$Q$ and $R$ manufacture $20 \%$,$30 \%$ and $50 \%$ respectively of the total output. The chances that a defective battery is produced by these machines are $1 \%$,$1.5 \%$ and $2 \%$ respectively. If a battery is selected at random from the production,then the probability that it is defective is

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

The probability that a year selected at random will have $53$ Mondays is