Finding Variance in Poisson distribution question

[sallu110]

Hello! Can anyone tell me how to solve this question?
Consider that X~ Poisson(μ) and P(X > 0) = e ^−1.5
Find the variance?

I need P(x =0) to use the formulae of Poisson distribution. But I don't have that!

 

[Dason]

You've got everything you need or at least enough to figure out the pieces that you need

 

[sallu110]

You've got everything you need or at least enough to figure out the pieces that you need

Okay this is roughly what I tried
P(X=0) = 1-P(X>0)
1- e^-1.5
= 0.77686

So P(X=0) = (e^(-variance)*variance^(0))/0!

0.77686 = e^(-variance )
taking natural log
-0.2524 = -variance
variance = 0.2524

But I don't think that P(X=0) = 1-P(X>0)...... Isn't it P(X=0) = 1-P(X<0)?