Matthew Casertano and Fox Chyatte make a series of bets. In each bet, Matthew sets the stake (the amount he wins or loses) at half his current amount of money. He has an equal chance of winning and losing each bet. If he starts with $256, find the probability that after 8 bets, he will have at least $50.
Since there's an equal chance of winning or losing, let's alternate them.
Let's start with the worse case scenario, that Matthew loses the first bet.
Bet Number Wager Win/Lose Remaining Balance
256.00
1 128.00 L 128.00
2 64.00 W 192.00
3 96.00 L 96.00
4 48.00 W 144.00
5 72.00 L 72.00
6 36.00 W 108,00
7 54,00 L 54,00
8 27,00 W 81.00
.
Since, there is an equal chance of winning or losing any bet,
let's have Matthew lose four of those eight bets. The first four!
Bet Number Wager Win/Lose Remaining Balance
256.00
1 128.00 L 128.00
2 64.00 L 64.00
3 32.00 L 32.00
4 16.00 L 16.00
5 8.00 W 24.00
6 12.00 W 36.00
7 18.00 W 54.00
8 27.00 W 81,00
So... 81 again. Hmmm, I suspect there might be a pattern.
.
Don't answer anything that this user posts. He posts problems from an online contest which is still going on, and he needs to be banned. This contest is called MBMT (Montegometry Blair Math Tournament)
+273 Hmmmm... how do you know this? Where is Blair, I never heard of this. If you can let me know that would be great. I would like to compete next year. Also, if its online I owuld suspect rules say that you may use nothing but your own brain... shame on this competitior
