Probability question

[marayuin1]

Hi,

I am really confused with a probability question and I would really appreciate your help.

Question: a) If the six-face dice is numbered by 1, 2, 3, 4, 5, and 6, but the eight-face dice is numbered by 1, 2, 3, 4, 5, 6, 6, and 6, what is the expected number if you roll each type of dice many times, respectively?
In this question, I did my calculations and I got an answer: E(X+Y)= E(X)+E(Y) = 3.5 + 4.125= 7.625. However, I am not very sure about it, because the question is not very clear to me. for example, do I have to find the sum value or the expected value for each die?

What really confuses me is part b)
Now if you randomly pick one dice from a black box with two six-face dices and one eight-face dice, what is the expected number you can roll?

Thank you!

 

[obh]

Hi Marayuin,

I agree with you, "what is the expect number" is not a good definition ... you expect to get all the numbers 1,2..6
It should be probably "what is the average number"... so 3.5 for the six-face dice and 4.125 for the eight-face dice. (no need to add to 7.625)
It may as well be what number occurs most frequently ..(mode)

 

[marayuin1]

I did some research on that, and actually the mean of a random variable is also known as its expected value.
Thanks for your help!!

 

[obh]

Okay ...
So you should calculate separately the mean of each dice.

 

[marayuin1]

Yes, and for the six-side the expected value=3.5 and for the eight side dice= 4.124.
However, I do not get the question b.
inside a box there are three dice: 2 six face dice, and 1 eight side die
Is the answer: 2/3*(3.5)+1/3*(4.125)
Does it seem right, I am frankly very confused?!

 

[obh]

Correct