Will your lucky symbol show up in thirty spins?

Question

A slot reel shows one of 20 equally likely symbols per spin, independently each time. You have one favorite symbol. What is the probability your favorite symbol appears at least once across 30 spins?

Accepted Answer

Each spin either shows your symbol (probability 1/20) or does not (probability 19/20). The spins are independent, so use the complement, your symbol never appears: P(	ext{never appears}) = \left(\frac{19}{20}ight)^{30} \approx 0.215. Therefore P(	ext{appears at least once}) = 1 - 0.215 \approx 0.785, about 79\%. Sanity check: the expected number of appearances is 30/20 = 1.5, and 1 - e^{-1.5} \approx 0.777, close to the exact 0.785. Notice this is a fixed-target problem: you track one specific symbol across 30 chances, so the count of spins is what matters. Takeaway. For "does my target a…

Will your lucky symbol show up in thirty spins?

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