Thank you for visiting The biathlon is a winter sport that combines cross country skiing and rifle shooting For this problem consider an event with five skiing phases split. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
a) The binomial distribution formula is
[tex]\begin{gathered} P(k)=(nbinomialk)p^k(1-p)^{n-k} \\ k\rightarrow\text{ number of successful trials} \\ n\rightarrow\text{ total number of trials} \\ p\rightarrow\text{ probability of successful trial} \end{gathered}[/tex]Therefore, in our case, since we need the probability of hitting 5 targets with 5 bullets,
[tex]\begin{gathered} P(5)=(5binomial5)(0.85)^5(1-0.85)^{5-5}=1*(0.85)^5(0.15)^0=(0.85)^2 \\ \Rightarrow P(5)=(0.85)^5=0.4437... \end{gathered}[/tex]The exact probability of event a) is (0.85)^5, approximately 0.4437
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