00:01
Hi, i'm david and i'm here to have you answering your question.
00:04
Now let me bring up your question here.
00:07
In this question we will win to play a game.
00:10
So will you roll a fair six -sided die three times independently? and we will count the number of the six appears here.
00:20
So if the six appears no time you lose $1, one time you win one, two times we win two, and three times we win, we don't know the case.
00:30
And we need to know once okay so that the game will be fair so i will call the x equal to the number under six appears in three rooms so remind you that we have the x followed by the binomial and b then the probability of x equal to k it will equal to the n choose k p power k and then one minus b power n minus k here we have totally three rules independently so n equal to the three probably you can the six on on each role will be one out of six so probability to gain the six we equal to one over six so from here we can see x followed by the binomial with the n equal to 3 be equal to 1 out of 6.
01:32
Now let's try to make a table for the x and the proper pithing the x.
01:37
X can have a 0, 6 appears, x can have 1, x can be 2, and x can be 3.
01:48
And this will be the proper being the x, and this will be the gain we have here.
01:55
Now for x to 0, it will apply the formula here.
01:57
Let me remove this one to the on the side further and we put some space here.
02:05
So that will be the gain.
02:07
Now for xo.
02:09
We have the n will be 3 to 0 and then 1 out of 6 power 0 and then 1 minus 1 of 6 out of 6 out of 6 power 3.
02:23
Then we do the calculation.
02:25
We will have this one will be 0 .1, 6 .6.
02:40
Number trial will be 3, 6x will be 0...