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Certain types of traders attempt to repeatedly buy and sell the same asset for a profit over a short time period, such as high-frequency “market makers”. For example, if you can repeatedly sell a stock for \$8.50 and buy it for \$8.49, you will make \$0.01 each time. This is known as arbitrage.

If this transaction succeeds with probability 99%, about how many times can this transaction be executed before the probability of at least one failure exceeds 50%?

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Imho that's more of a probability question than finance really.

If you take $N$ attempts, then the probability of at least one (or more) failures is the complementary probability of never failing on those $N$ attempts:

$p=1-p_{pass}^N$

Solving for $p=50\%$, you need to evaluate $p_{pass}^{N}=0.5$, where $p_{pass}=0.99$, getting that $N\geq 69$.

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