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There are three shooters $A$, $B$, $C$ who are shooting a target $D$ at the same time. Consider the following three events:
A)$E_a$=Shooter $A$ hits the target
B) $E_в$=Shooter $B$ hits the target
C) $E_c$=Shooter $C$ hits the target
Assume $P(E_a) =0.9$, $P(E_в) =0.8$, $P(E_c)=0.7$ and these three events are mutually independent.
What is the probability that target D was hit by some players?

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  • $\begingroup$ What is the probability D was not hit by any player? $\endgroup$
    – Henry
    Dec 6, 2020 at 13:10

1 Answer 1

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The probability that none of the shooters hit the target is

$$(1-0.9)(1-0.8)(1-0.7)=0.006$$

Thus the requested probability is its complement: $0.994$

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