Solving Dice Throwing Problem: Is Shared Outcome Higher/Lower Than Expected?

[b-boy]

Hi,I have the following problem that i don't know how to start solwing. I want to know if an occurence of my dice throwing outcomes is higher or lower then expected. I'll try to describe the problem as much as i can but if i miss something please feal free to ask. All I am looking for is a kick in the right direction.
let say i have two sets of dices one is black (B) the other is white (W). Now when i throw black dices (let say there are b=8 black dices and w=5 white ones) i get an outcome like this B={2,4,2,1,1,4,5,6 }. Then i throw the white ones and i get W={2,1,1,3,3}. My question is : given that B and W share 3 outcomes (shared outcomes: 1,1,2), is that more or less then expected. how would i start modeling my particular problem. Clearly i have a binom. distr. here but what confuses me is the numbr of dices in B and W.
Is it clear what i am looking for?? So I am interested to know if the intersect of shered outcomes is something that i would expect by chance alone or not. My model should only depend on b and w. Can someone please help me get started.thank you baxy

ps this is a post similar to the one on MHF but apperently the site as been compromizd so i have reposted it here.

 

[Valkarie]

The best way to start solving this problem is to use a statistical test, such as the chi-squared test. The chi-squared test is used to determine if two variables are statistically significantly associated with one another. In this case, you would use the chi-squared test to compare the number of shared outcomes between B and W against the expected number of shared outcomes, based on the total number of dices in each set. You would calculate the expected number of shared outcomes by multiplying the probability of an outcome in B with the probability of an outcome in W. For example, if there were 8 black dices and 5 white dices, the probability of a shared outcome would be 8/13 * 5/13 = 0.35. This would give you the expected number of shared outcomes. Then you would compare this expected number of shared outcomes against the actual number of shared outcomes. If the actual number is greater than the expected number, then it means that the occurrence of the shared outcomes is higher than expected, and vice versa. You can then use the chi-squared test to determine if the difference is statistically significant.