Question 1162805: Gillian and Jonathan are playing a coin tossing game. Each one starts with 3 looneys. At each turn,
one of the players takes one of his looneys and tosses it. If it comes up heads, the tosser loses, and
must give the looney to the other player. If it comes up tails, the tosser wins, and gets to keeps the
looney. In either case the loser has to toss his or her looney on the next turn. If one person loses all
their looneys, the game is over.
(a) Suppose that Gillian and Jonathan decide that if the game is not over by the fifth turn, they will
stop anyway. Let Jonathan have the first toss.
i. Write out all the elementary events in the sample space for this experiment. Would they be
equally likely?
ii. Let Fi be the event that the game is over after i turns (i = 1, . . . , 5). Find the probability of
each Fi
. Should these probabilities sum to 1?
iii. Let Ei be the event that each player still has three looneys after the i
th turn. Find the
probability of each Ei
. Should these probabilities sum to 1?
iv. Find the probability that Gillian loses all her looneys.
(b) Suppose that Gillian and Jonathan had not decided to end the game after five turns. Is it possible
for the game to go on forever? What would be the probability that the game never stops?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
In my life, I saw tens of thousands of Math problems, and solved thousands of them,
and I firmly believe that there is no Math problem longer than 5 lines of standard format.
All the rest is EITHER essays OR nonsense.
More concretely, it is not clear to me, for what purpose/purposes this post was submitted to the forum ?
If a person wants to learn on solving Probability problems, he (or she) should start from basic problems,
which all and always are short in their formulation.
Also, the laws of the nature are such that nobody will not only solve, but even read so long text
without a vital necessity, excepting it is of extraordinary interest, which is definitely not the case.
If a visitor does expect that the tutors will work instead of him (or her), then the visitor makes a HUGE mistake.
Our goal at this forum is not to work instead of students, making their job, but to TEACH them.
Assuming that the students are able to learn and really want to do it . . .
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