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Easy · Probability & Statistics · Quant Trader interview question · probability, union-bound, boole's-inequality, risk-management
As a risk manager, you are evaluating a trading strategy that involves multiple independent events. Suppose you have $k = 10$ events, $A_1, A_2, ..., A_{10}$. Each event $A_i$ has a probability of occurring of $P(A_i) = 0.01$. Using Boole's inequality (also known as the union bound), what is the upper bound on the probability that at least one of these events occurs, i.e., what is the upper bound on $P(\bigcup_{i=1}^{10} A_i)$?