Question 483897
.
The probability that a bullet fired from a point will hit the target is 1/3. 
Three such bullets are fired simultaneously towards the target from that very point. 
What is the probability that the target will be hit?
~~~~~~~~~~~~~~~~~~~~~~~~~~



        For this problem, and for many other similar problems, there a standard way to teach

        and a standard way to get a simple, short, elegant and educatively valued solution,

        which I place below.



<pre>
The probability to hit the target with one bullet is 1/3.

Hence, the probability do not hit the target with one bullet is 1 - 1/3 = 2/3.


Therefore, the probability do not hit the target with three bullets is {2/3)^3 = 8/27.


It means that the probability that the target will be hit by at least one of the bullets

is the complement to 8/27, i.e.  1 - 8/27 = 19/27.


At this point, the problem is just solved completely.


<U>ANSWER</U>.  The probability that the target will be hit is 19/27.
</pre>

Solved.


You should know this method.


It is how this problem is expected to be solved.


It is what your teacher does expect from you.