Find the expected value of X. (PLEASE HELP, I DON'T GET THIS CRAP)?

Question

Two fair dice are tossed. The random variable X is defined to be 10 if the numbers showing are different, and 100 if the numbers showing are the same.

Answer 1

A dice has 6 faces.
Prob that the two dice show equal = 1/6.
So Prob that the two dice show unequal = 5/6.
So the expected value of X is

E(X) = 10*5/6 + 100*1/6 = 150/6 = 25.

Answer 2

First roll one of the dice and get some result. Then roll the second. What's the chance that they'll match?

Regardless of what we rolled for the first die, we have a 1/6 chance of matching up (since there are 6 different sides).
5/6 of the time we will not match.

so we get 100 once, and 10, 5 times.
(100 + 10 + 10 + 10 + 10 + 10)/ 6
= (150/6)
= 25

or
100 * 1/6 + 10 * 5/6
= 100/6 + 50/6
= 150/6
= 25

Answer 3

Well, it sort of depends how many faces there are on the dice. I think that they are using expected value here in the sense of average after a large number of rolls so, assume they are 4 sided dice, 1/4 of the rolls will have the same number, average X is 130/4.
expectation for X is 35. Best I can guess.

Answer 4

Hmm-m. Me either.

However, one die of a pair of dice has six numbered sides.
And there are two die in a pair of dice.

So there are six times six possible combinations of numbers
= 36.

Of those six are matching numbers = 6 x 100 = 600
those remaining are 36 - 6 = 30. 30 x 10 = 300

so the maximum number is 900.

The average number is 21 / 6 x 21 / 6 = 12.25 total.

I don't know if this helps any, but I tried.

Zah

Answer 5

there are 36 possibilities....
6 are doubles (same) 30 are not

so, you have a 1/6 chance of getting 100
you have a 5/6 chance of getting a 10
[ with 6 chances... you get 1 double and 5 not doubles)

their sum is ( 1*100 + 5*10) = 150
150 divided by 6 tries is 25 times

you can expect a "average" value of 25 for each roll although you can never achieve that value through any single roll....

hope it makes sence

Answer 6

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Answer 7

I almost give the exact same answer with Leltos. Anyway, his answer is the best I can think of. Sorry.

Answer 8

I admire your candor. I don't get it either. Be back later to learn.