TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/2.5

Target

If the probability of hitting a target is 1/5 , and ten shots are fired independently, what is the probability of the target being hit at least twice? What is the conditional probability that the target is hit at least twice, given that it is hit at least once?

Lösungsvorschlag von Gittenburg

--Gittenburg 18:51, 21. Okt. 2019 (CEST)

$P(A)=1-\left({\frac {4}{5}}\right)^{10}-{\frac {1}{5}}\left({\frac {4}{5}}\right)^{9}{\binom {10}{1}}\approx 0.624$

Given that it is hit at least once:

$P(A)=1-\left({\frac {4}{5}}\right)^{9}\approx 0.866$