Question

Help with probability:

An urn contains 10 objects labeled from 1 to 10. A game consist in taking those objects
and it finish when the one labeled with 1 comes out. ¿ What is the probability for finishing the game if we pull 5 objects randomly:
a) at the same time
b) one by one without reposition
c) one by one with reposition

I know that a) is C(1,5)/10 = 1/2
I was thinking that for b, the prob. should be 1/10+1/9+1/8+1/7+16/, but the answer dont match. I think i'm missing the conditional probability part.

Thanks

Answer 1

b) Using the formula for sampling without replacement gives:
\[P(finishing)=\frac{\left(\begin{matrix}1 \\ 1\end{matrix}\right)\left(\begin{matrix}9 \\ 4\end{matrix}\right)}{\left(\begin{matrix}10 \\ 5\end{matrix}\right)}=\frac{1}{2}\]

Answer 2

The answers according the book are a) 1/2, b) 0.1 c)9^4/10^4

Answer 3

i can do it the donkey way

Answer 4

b) one by one without reposition
9 choices for the first one
8 for the second
7 for the third
6 for the fourth
1 for the fifth

Answer 5

\[\frac{9}{10}\times \frac{8}{9}\times \frac{7}{8}\times \frac{6}{7}\times\frac{ 1}{6}\]
another simpler way to think about it is that no one outcome is favored, so the probability you get a 1 on the fifth pull is exactly the same as it is on the first pull, namely \(\frac{1}{10}\)

Answer 6

solution to the last should now be obvious
it is \(\frac{9}{10}\) for all four choices then \(\frac{1}{10}\) for the fifth

Answer 7

Got it, thanks.

Answer 8

The solution for b) in the book and by @satellite73 gives the probability of ending the game on the last draw. My solution gives the probability of ending the game on any of the five draws. Is the question unclear on this point?

The solution by @satellite73 results in 9^4/10^5. this does not agree with the answer from the book that @Juarismi posted.

Answer 9

c) The solution by @satellite73 results in 9^4/10^5. this does not agree with the answer from the book that @Juarismi posted.