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MathNet 2026 — Part 01 Question 124

Math Olympiad Vault · MathNet 2026 — Part 01

Question 124

As of today, the great gambler Carlo Pietro decided to attend casinos daily. On the first day, he will bet on a game whose probability of winning is equal to $\frac{1}{2}$. In the second, third and fourth days, he will bet on different games whose win odds are, respectively, equal to $\frac{1}{3}, \frac{1}{4}, \frac{1}{5}$ and so on in the following days.
a) What is the probability that it has not won until the third day?
b) What is the probability that he has not won until the fifth day?
c) What is the probability that it has not won until the $2013^{\underline{0}}$ day?