mathsteve
posted by andre
When Mr. Lucky starts betting, he has 3 dollars. On any bet, he wins with probability 1/3 and loses with probability 2/3. If he wins
a bet, the total amount of money he has triples. If he loses a bet, he
loses 2/3 of the total amount of money he has. Mr. Lucky’s objective
is to walk away with 27 dollars in his pocket, and he can keep playing as long as he has at least 3 dollars. What is the probability that he reaches his objective? Express your answer as a common fraction.
math  Steve, Tuesday, July 5, 2016 at 4:41am
1/10 to end up with exactly 27
6/10 to end up with at least 27
4/10 to lose
The answer is 1/7, but I don't know how to get it.

Steve
Hmmm. I drew a tree with all possible outcomes, but I forgot to weight each branch with its probability. Try doing that and see what happens. I'll try to get back later.
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