Solving a Probability Question with Poisson Distribution

[persist911]

Homework Statement

I am solving a particular probability question using Poission distributin after the Solving I get an equation

Homework Equations

 1.67 =  e^-a (1/1-a)

I ought to get the value of a from the equation but I was Unable to go further from here .

The Attempt at a Solution

I have tried expaning e^-a using series but no luck . I am totally stuck.

 

[CompuChip]

Assuming you meant
$$1.67 = \frac{e^{-a}}{1 - a}$$
there is no "nice" solution.
It can be written as
$$1 - a = W_n(- a / e) \qquad (n \in \mathbb{Z})$$
where W_n the so-called product-log function, i.e. the solution for w of z = w e^w. So that doesn't bring you much further, I'm afraid... are you sure you need to solve this analytically and - if so - the equation is correct?