Thread: Die experiment

Can someone please help me out for this question.

Consider an experiment where we roll a single die and observe the # of dots. Thus,m our sample space is S = 1,2,3,4,5,6 . Suppose that the die is not fair and that P (i) = k/i for i = 1,2,3,4,5,6. What is the value of k?

I don't understand what it means by the die not being fair. What would be the steps to solve such a problem? Would it be something along hte lines of:

P (i) = k/6

since it says we observe the # of dots do we just add the dots together?

P (i) = 21/6?


I'm just making a guess here but I'm not sure how to even start with this.

Thanks.

Originally Posted by agent2421

Can someone please help me out for this question.

Consider an experiment where we roll a single die and observe the # of dots. Thus,m our sample space is S = 1,2,3,4,5,6 . Suppose that the die is not fair and that P (i) = k/i for i = 1,2,3,4,5,6. What is the value of k?

I don't understand what it means by the die not being fair. What would be the steps to solve such a problem? Would it be something along hte lines of:

P (i) = k/6

since it says we observe the # of dots do we just add the dots together?

P (i) = 21/6?


I'm just making a guess here but I'm not sure how to even start with this.

Thanks.

For a fair die the probability of the outcomes are equaly likely. A die is not fair if the probability of each outcome is not the same. Since one of 1, .., 6 must be the result of rolling the die for a fair die p(i)=1/6, i=1..6.

This die has P(1)=k/1, P(2)=k/2, p(3)=k/3), p(4)=k/4, p(5)=k/5, p(6)=k/6

but when you roll the die the result must be one 1, 2, 3, 4, 5, 6 so:

p(1)+p(2)+..+p(6)=1

and you may use this to determine what value k must have.

CB

I'm not sure if this is correct or not but I'm assuming you mean for a fair die each outcome will have a 1/6 probability. Since this is not fair it will be distributed through all the numbers meaning:

P (1)= k/1 + P (2) = k/2 + P (3) = k/3 + P(4) = k/4 + P(5) = k/5 + P (6) = k/6

Therefore

P (1) = 1/1 + P (2) = 2/2 + P (3) = 3/3 + P (4) = 4/4 + P (5) = 5/5 + P (6) = 6/6

would that be right or no? The problem is that k is different in each one so I think i'm still misunderstanding what you are trying to say.


Thanks.

You've been told that P(i) = k/i. Therefore:

P(1) = k
P(2) = k/2
P(3) = k/3
P(4) = k/4
P(5) = k/5
P(6) = k/6

Since these 6 possibilities are the only ones that exist, you know that
P(1) + P(2)+ P(3) + P(4) + P(5) + P(6) = 1.

Now you can solve for k.

Actually I didn't read that it all has to equal to 1. So just by plugging in numbers i came to the conclusion that k has to be somewhere around 0.4.

So i did:

0.4/1 + 0.4/2 + 0.4/3 + 0.4/4 + 0.4/5 + 0.4/6 = 0.98 so it's fairly close to 1... Is there an actual way of doing the math though to make it 1? 0.4082 reaches a bit over 1 but is there a way or formula to get a concrete answer... I'm pretty sure this is on the right track but once again it's just by plugging in numbers to try and make it equal to 1.

Originally Posted by agent2421

Actually I didn't read that it all has to equal to 1. So just by plugging in numbers i came to the conclusion that k has to be somewhere around 0.4.

Really thus .

I'm sorry but where do you get the 49 from? I feel really stupid for not understanding this right away lol.

Originally Posted by agent2421

I'm sorry but where do you get the 49 from? I feel really stupid for not understanding this right away lol.

Can you add