Thread: probability box game problem.

a dude make the choice of selecting one of twenty six boxes which could contain 1 of the #'s below:

.01
1
5
10
25
50
75
100
200
300
400
500
750
1,000
5,000
10,000
25,000
50,000
75,000
100,000
200,000
300,000
400,000
500,000
750,000
1,000,000

The dude must then open other boxes, which gives both the dude and his opponent, the dudes girl, information about amounts that are not in the box. After the dude opens a certain number of boxes, the dudes girl makes an offer to steal the box for a certain amount of money, which the dude can accept (okay) or reject (no okay). If the dude okays, then this thing is over; if the dude rejects, then this thing continues with more boxes being opened.

a When this thing starts, what is the probability the dude has chosen a box that is worth #100,000 or greater?
b In one game, the dude has opened boxes with #100, #200, #500, #75,000, #100,000, #200,000, and #500,000. What is the probability the dude has chosen a box that is worth #100,000 or greater?
c As long as a dude does not open the #1,000,000 box, give the function that describes the probability of having the #1,000,000 box given that the dude has opened n boxes thus far.

....so please help me with part c, especially if i'm not correct about parts a & b.

so this is what I came up with:

for a:
100,000 or greater is this (100,200,300,400,500,750,1000) so 6
and the maximum amount of numbers are 26

and he uses 6 in 26 proportion of getting a number 100,000 or greater. (6/26)
:: 3/13

is it this simple for b?
so, 7 opened boxes, 100000 >= is 3/7
there are 3 that are > 100000

and i'm not sure for part c. Please help.

...and then below is, d e and f, and i'm not sure how to solve those parts.

(d) Part of the dudes girl's job is to decide how dangerous a dude is

willing to be. Let's imagine 2 dudes, Bob and Dylan, who have

identical situations (same boxes opened, same offer from the dudes

girl). Bob immediately decides to reject the offer. Dylan waits for a

long time, seems like hes going to take the okay, and then denies it.

is there anything to say about the offer and A's and B's decisions?

idea: ..could be like the lotto



(e) Its easily seen that by knowing the type of player helps the

dudes girl. So, how can the dudes girl try to know whether the player

is more like player Bob or player Dylan early on?



(f) think about a time where the another player has five boxes alive:

#1,000, #10,000, #20,000, #400,000, and #750,000. She's offered the

expected monetary value of the boxes in play, and denies the offer.

Later, she says that if she was offered #10,000 more, then she would

have taken the okay. So what can be said about the bounds of the

utility of taking part in this thing? Use a set of inequalities.