Answer
There will be $11$ trials; $(11,0.95)$
Work Step by Step
Set $P$ in the given formula equal to $0.95$. Multiply the denominator on both sides, and distribute all the terms and combine. Then isolate the $x$-term on one side and divide to solve.
$0.95=\frac{0.9x-0.4}{0.9x+0.1}$
$0.95(0.9x+0.1)=(\frac{0.9x-0.4}{0.9x+0.1})(0.9x+0.1)$
$0.95(0.9x+0.1)=0.9x-0.4$
$(0.95)(0.9x)+(0.95)(0.1)=0.9x-0.4$
$0.855x+0.095=0.9x-0.4$
$0.095+0.4=0.045x-0.4+0.4$
$0.095+0.4=0.045x$
$0.495=0.045x$
$x=11$
