Calculating probability of an event. The probability that someone catches a flu in a month is 1/10. We assume that he can catch the flu only once per month and he is cured by the end of the month he caught the flu. What is the probability that someone catches a flu in two or more of the three months from September through November ?

Let $X_i=1$ if you catch a flu in month $i$. Then $X_i$ is a bernoullian r.v. with $P(X_i=1) = 1/10$.

Let $Y = X_9+X_{10}+X_{11}$. Then $Y$ is a binomial distribution with parameters $n=3$ and $p=1/10$. So $$P (Y \ge 2) = P (Y = 2) + P (Y = 3) = 3 \left(\frac{1}{10}\right)^2 \left(\frac{9}{10}\right) + \left(\frac{1}{10}\right)^3$$