# A (probably very basic) question...

#### jdrewind

##### New Member
Hello,

Sorry if this is not the correct place to post this. I have a binomial stats question that I just cannot get to grips with at all and I'm in desperate need of some guidance! The question is...

A box contains 1000 coins, some are the gold and the rest silver. Suppose we sample 10 and find that 3 are gold. Test the hypothesis that the true number of gold coins in the box is exactly 500. What is the p-value for this hypothesis?

Can anyone please point me in the right direction here?!

Thank you,
Joe

#### rogojel

##### TS Contributor
hi,
you need two steps: 1. what is the probanility of picking a gold coin if 500 out 1000 are gold? and 2. what is the probanility of picking 3 gold coins out of 10 provided the probanility of picking a gold coin is what you calculated in step 1.

regards

#### jdrewind

##### New Member
hi,
you need two steps: 1. what is the probanility of picking a gold coin if 500 out 1000 are gold? and 2. what is the probanility of picking 3 gold coins out of 10 provided the probanility of picking a gold coin is what you calculated in step 1.

regards
Thank you. I had thought obviously if there are an equal number of silver and gold then that would be 0.5 and then there would be a 0.1171875 chance of getting three golds from ten picks. I've just checked though and apparently the answer should be 0.34...something is going way over my head!

#### rogojel

##### TS Contributor
hi,
I think for the p-value you calculate the probability of getting 3 or fewer gold coins, not the probability of getting exactly 3 and that would make a p-value of 0.17. However, for some reason the solution you were given assumes two a sided test so it gives you the probanility of being under 4 OR over 7 - which is then 2*0.17=0.34 - in my opinion this is wrong.
regards