In a game where you throw a dart at a circular target, if the probability of hitting the bullseye is 0.05, what is the probability of hitting the bullseye at least once in 20 tries?
Instruction: Assume twenty independent dart throws with constant bullseye probability 0.05. Calculate the probability of at least one bullseye and state the modeling assumptions.
Context: This question tests the candidate's application of binomial distribution to a practical problem.
Updated
Official answer
Assume twenty independent throws, each with bullseye probability 0.05. The probability of no bullseyes is 0.95^20, so P(at least one) = 1−0.95^20 ≈ 0.641514, or 64.15%.
The target's circular shape is irrelevant once the hit probability is supplied; no uniform spatial-landing assumption is needed. Learning, fatigue or shared conditions could change the per-throw probabilities or dependence. The result is conditional on the stated model, not a guarantee for a particular player.