If $P(X=x)=c\left(\frac{2}{3}\right)^x ; x=1,2,3,4, \ldots$ is a probability distribution function of a random variable $X$, then the value of $c$ is

In a non-leap year, the probability of getting 53 Sundays or 53 Tuesdays or 53 Thursdays is

The equation of the parabola with $x+2 y=1$ as directrix and $(1,0)$ as focus is

If $A$ and $B$ are two events in a random experiment such that $P(A)+P(B)=2 P(A \cap B)$, then