If the probability of an authentic laying goose is 0.83, find the probability of getting a laying goose on or before the fourht trial.

I think that answer is:
(0.17)(0.17)(0.17)(0.83)=.00407

*the answer needs to be rounded to three significant digits*

4 answers

Assuming that you are picking your geese from a yard full of an infinite number of geese , the chances of not getting a good one are the same for all four picks and are .17 indeed
so the chances of not getting at least one good one are
.17^4 = .000835
The probability of getting at least one good one is therefore 1 - .000835
= .999 to three significant figures.
Thank you so much that makes perfect sense but I forgot to say that there are 6 geese not an infinate amount.
Well, the way your question is worded, the probability does not seem to change as you run out of geese, so my answer would not change.
But beware, if they said 4 out of 6 were layers, the probability would be 100%
I mean 5 out of THIS six were layers.