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IAI November 2013 Question 11 (i) (a)

S

Shreeraj Gandhi

Member
Ajoy is an avid cricket fan and he wants to watch the next India vs. Australia is to be held in his city. He has Rs. 300 and the minimum price of a ticket to the stadium for that particular match is Rs. 800. One of his friends has agreed to make a series of bets with him with Rs X at stake. If Ajoy bets Rs X, he wins Rs X with probability 0.45 and loses Rs X with probability 0.55.
i) Find the probability that he wins Rs. 800 before losing all of his money if
a) he bets Rs 100 each time.

Can someone please explain me the solution to this question?
 
Wow, what a great question! He has 300 Rs and needs to get to 800 before 0. Easier to work in units of 100 Rs, he has to get to 8 before 0. I would define pi = P[of winning eventually| he is on i]. So, p8 = 1 and p0 = 0
p7 = 0.45p8 + 0.55p6 = 0.45 + 0.55p6
p6 = 0.45p7 + 0.55p5
....
p1 = 0.45p2 + 0.55p0 = 0.45p2 + 0.55
Substitute p1 into p2, p2 into p3
Also, substitute p7 into p6, p6 into p5, p5 into p4, p4 into p3
The answer is p3.

There's probably some kind of result for problems like this based on geometric distributions or something. I would post the question (and my response) on the CT3 forum, see if one of the other tutors has a more elegant way of doing it (I suspect they may have!)

Good luck!
John
 
John Potter said:
Wow, what a great question! He has 300 Rs and needs to get to 800 before 0. Easier to work in units of 100 Rs, he has to get to 8 before 0. I would define pi = P[of winning eventually| he is on i]. So, p8 = 1 and p0 = 0
p7 = 0.45p8 + 0.55p6 = 0.45 + 0.55p6
p6 = 0.45p7 + 0.55p5
....
p1 = 0.45p2 + 0.55p0 = 0.45p2 + 0.55
Substitute p1 into p2, p2 into p3
Also, substitute p7 into p6, p6 into p5, p5 into p4, p4 into p3
The answer is p3.

There's probably some kind of result for problems like this based on geometric distributions or something. I would post the question (and my response) on the CT3 forum, see if one of the other tutors has a more elegant way of doing it (I suspect they may have!)

Good luck!
John
Click to expand...

Thanks
 
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