Shooters

In army regiment are six shooters. The first shooter target hit with a probability of 49%, next with 75%, 41%, 20%, 34%, 63%. Calculate the probability of target hit when shooting all at once.

Correct result:

p =  98.53 %

Solution:

$$\begin{gathered} p_1=0.49+0.75-0.49\cdot 0.75=0.873 \\ {p}_2=p_1+0.41-p_1\cdot 0.41=0.925 \\ {p}_3=p_2+0.2-p_2\cdot 0.2=0.94 \\ {p}_4=p_3+0.34-p_3\cdot 0.34=0.96 \\ {p}_5=p_4+0.63-p_4\cdot 0.63=0.985 \\ p=100\cdot p_5\doteq 98.53\mathrm{\%} \end{gathered}$$

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