1. ## Algebraic Methods

'The age of a machine, x, in years, is related to the probability of breakdown, y, by the formula

x = 3 + ln(y/1-y)

Determine the probability of breakdown for 1, 3 and 10years.

2. Originally Posted by gav1981

'The age of a machine, x, in years, is related to the probability of breakdown, y, by the formula

x = 3 + ln(y/1-y)

Determine the probability of breakdown for 1, 3 and 10years.
You want to isolate y in this equation...

$e^{x-3}=\frac{y}{1-y}$

$e^{x-3}-ye^{x-3}=y$

$e^{x-3}=y(e^{x-3}+1)$

$y=\frac{e^{x-3}}{e^{x-3}+1} \Rightarrow \frac{1}{1+e^{3-x}}$

Now, plug and chug for values of x.