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The probability of an arrow reaching a target is 0.85. How many times the arrow must be shot in order to hit the target 340 times?
A. 289
B. 400
C. 500
D. 600

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Last updated date: 13th Jun 2024
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Answer
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Hint: We will write the given probability in terms of fraction and then in percentage. Here, 0.85 implies 85% of total shots. Let the total shots be $x$, then we will solve the equation 85% of total shots equal to 340 to get the required answer.

Complete step-by-step answer:
The probability of hitting a target is 0.85 which is equivalent to $85\% = \dfrac{{85}}{{100}}$.
This implies the person hits 85 targets out of 100 shots.
Let the total number of shots be $x$
Now, according to the question, we have
$\Rightarrow$ \[\dfrac{{85}}{{100}}x = 340\]
Cross multiply the above equation.
$\Rightarrow$ $85x = 34000$
Divide both sides by 85
$\Rightarrow$ $x = \dfrac{{34000}}{{85}} = 400$
Hence, the times the arrow must be shot 400 times in order to hit the target 340 times.
Thus, option B is correct.

Note: Probability of an event is the ratio of number of favourable outcomes to number of total outcomes. If the probability of an event is $\dfrac{{85}}{{100}}$, this implies that the number of targets hit are 84 when the number of shots are 100.