Answer
See the picture.
Work Step by Step
$P(4)=x$
$P(3)=2\times P(4)=2x$
$P(2)=2\times P(3)=4x$
$P(1)=2\times P(2)=8x$
$P(1)+P(2)+P(3)+P(4)=1$
$8x+4x+2x+x=1$
$15x=1$
$x=\frac{1}{15}$
$P(4)=\frac{1}{15}$
$P(3)=\frac{2}{15}$
$P(2)=\frac{4}{15}$
$P(1)=\frac{8}{15}$
