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Difficulty: MediumSingle Event Probability

During a land navigation exercise, an instructor maps out 150 possible waypoint coordinates. Of these waypoints, 45 are located in dense forest, 35 are in open terrain, 50 are near water features, and the remaining waypoints are on elevated ridges. If a cadet is randomly assigned one waypoint coordinate, what is the probability that it is located on an elevated ridge? (Express your answer as a simplified fraction)

Answer: 2/15 / 2 / 15

Answer

2/15
The correct probability is found by dividing the number of ridge waypoints (20) by the total number of waypoints (150). Simplifying the fraction 20/150 yields 2/15.

Step-by-Step Solution

1
Determine the total number of possible outcomes.
Total waypoints = 150.
The denominator for a single event probability calculation is the total number of items in the set.
2
Calculate the number of favorable outcomes (elevated ridge waypoints).
150 - (45 + 35 + 50) = 150 - 130 = 20 waypoints on elevated ridges.
You must subtract the sum of all known waypoint categories from the total to find the unknown remainder.
3
Set up the probability ratio and simplify the fraction.
20 / 150 simplifies to 2 / 15.
Probability is the number of favorable outcomes divided by total outcomes. ASVAB format requires fractions to be reduced to their lowest terms.

Key Concept

Single Event Probability
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Topics

Single Event Probability

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