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*
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.
To find the probability of getting a laying goose on or before the fourth trial, you can calculate the complementary probability of not getting a laying goose up to the fourth trial and subtract it from 1.
Let's start by finding the probability of not getting a laying goose on each trial. The probability of not getting a laying goose on a single trial is equal to the complement of the probability of getting a laying goose, which is 1 - 0.83 = 0.17.
Since the events are independent, you can multiply the probabilities together for each trial. In this case, we want to calculate the probability of not getting a laying goose on all four trials, so we multiply 0.17 by itself four times:
0.17 x 0.17 x 0.17 x 0.17 = 0.001857641.
However, we want the probability of getting a laying goose on or before the fourth trial, so we need to subtract this value from 1:
1 - 0.001857641 = 0.998142359.
Now we need to round this answer to three significant digits. Since the fourth digit is less than 5, we can simply round down:
0.998.
Therefore, the probability of getting a laying goose on or before the fourth trial is approximately 0.998.