Question

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

Answer 1

Hint: We have the probability of an arrow reaching a target. This means ${\text{85% }}$ of the arrows shot hit the target, so to get the Number of times one should attempt to hit the target so that 340 times the arrow hits the target, can be written as ${\text{85% }}$ of the total number of shots is equal to 340, and on solving we will get the total number of shots.

Complete step by step Answer:

We are given that the probability of an arrow reaching a target is 0.85. This means 85 arrows out 100 arrows shot will hit the target. Let us consider ${\text{x}}$to the number of times the arrow must be shot in order to hit the target 340 times. Then according to the given probability, 340 is ${\text{85% }}$of ${\text{x}}$. Using this we can write,
${\text{340 = }}\dfrac{{{\text{85}}}}{{{\text{100}}}}{\text{ $\times$ x}}$
Solving for x, we get,
${\text{x = 340 $\times$ }}\dfrac{{{\text{100}}}}{{{\text{85}}}}{\text{ = 400}}$
So, the arrow must be shot 400 times in order to hit the target 340 times.
Therefore, the correct answer is option B.

Note: The concept of probability is used in this question. The basic algebra of percentages is also used to solve this problem. We must understand that $0.85 = \dfrac{{85}}{{100}}$ and this is equal to 85%. The probability of an event is defined as the ratio of the number of events with favorable outcomes to the total number of events. An alternate approach to this problem is that the number of arrows shot will be greater than the number of arrows that hit the target. We can check with the options like which option gives 340 when we calculate 85% of each option.