# 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:

$p_1 = 0.49+0.75-0.49 \cdot 0.75 = 0.873 \ \\ p_2 = p_1+0.41-p_1 \cdot 0.41 = 0.925 \ \\ p_3 = p_2+0.2-p_2 \cdot 0.2 = 0.94 \ \\ p_4 = p_3+0.34-p_3 \cdot 0.34 = 0.96 \ \\ p_5 = p_4+0.63-p_4 \cdot 0.63 = 0.985 \ \\ \ \\ p = 100 \cdot p_5 \doteq 98.53 \%$

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