Probability. (1 Viewer)

[Lazarus]

Harder Probability.

I came across this question and thought it was good -

A dark cupboard contains a mixture of black and white socks in the proportion of 1 white sock to 2 black socks (i.e. 1/3 of the socks are white). You cannot see into the cupboard. You can reach into it and pull out one sock at a time, and you are looking for a black sock. Assume that there are so many socks that the probability of finding a particular sock is constant.

How many socks do you expect to pull out to ensure that you have a black one with probability greater than 99%?

 

[McLake]

There is a hint hidden in my post (press quote to see it)

<Hint: (2/3)^n gt= 0.99>
<nb gt = "greater than">

 

[McLake]

And the answer is hidden in this post (thanks to whoever came up with this idea)

<Answer NB: gt = "greater than">
<Answer NB: lt = "less than">
<Answer 1 - (1/3)^n gt= 0.99>
<Answer (1/3)^n lt= 0.01>
<Answer log ((1/3)^n) lt= log(0.01)>
<Answer nlog(1/3) lt= -log(0.01)>
<Answer n lt= -log(0.01)/log(1/3)>

Final Answer: 4

 

[Lazarus]

Mm, well done McLake, but the final answer is 4, not 5. Unless I've erred.

 

[McLake]

Well, look at my working and check (unless I made a mistake with the last calculation) ...

 

[Lazarus]

Originally posted by McLake
Well, look at my working and check (unless I made a mistake with the last calculation) ...

I think your final line should instead contain a 'less than' operator; the original mistake probably occurred a few lines before that.

 

[McLake]

Opps, I hate inequalities, I always forget to flip them with negative signs ...