Alarm systems

What is the probability that at least one alarm system will signal the theft of a motor vehicle when the efficiency of the first system is 90% and of the independent second system 80%?

Correct answer:

p =  98 %

Step-by-step explanation:

$$\begin{gathered} p_1=90\%=\frac{90}{100}=\frac{9}{10}=0.9 \\ {p}_2=80\%=\frac{80}{100}=\frac{4}{5}=0.8 \\ p=100\cdot (p_1+p_2-p_1\cdot p_2)=100\cdot (0.9+0.8-0.9\cdot 0.8)=98\% \end{gathered}$$

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