- #1
davon806
- 148
- 1
Homework Statement
There are 20 eggs in the box and three of them are rotten,
If I pick eggs without replacement calculate P(my first rotten egg comes at my k-th pick)
Homework Equations
The Attempt at a Solution
I come up with two solutions:
(1)As there is no replacement,I can use the hypergeometric distribution
So,P(my first rotten egg comes at my k-th pick) = C(17,k-1)C(3,1) / C(20,k)
(2)I can use the multiplication theorem for conditional probability,i.e.
P(my first rotten egg comes at my k-th pick) = (17/20)(16/19)...(3/21-k)
Let assume I got a rotten egg in the 4-th trial,
Using method (1),P = 8/19
Using method (2),P = 2/19
Similarly,for the 5-th trial
(1) yields P = 35/76
(2) yields P = 7/76
In each case,(1)/(2) = k,where does this factor k come from?Both of them seems make sense so which one is wrong?
Thanks :)