A logistics officer is inspecting a shipment of 120 combat helmets. The shipment contains … — Armed Services Vocational Aptitude Battery (ASVAB)

A logistics officer is inspecting a shipment of $120$ combat helmets. The shipment contains $45$ large helmets, $35$ medium helmets, $24$ small helmets, and the remaining helmets are extra-large. If the officer randomly selects one helmet for quality control, what is the probability that it is an extra-large helmet? Express your answer as a fraction in simplest form.

Answer: 2/15 / 2 / 15

Answer

2/15

The correct answer is derived by first finding the number of extra-large helmets. Subtracting the known sizes from the total yields

120 - 104 = 16

extra-large helmets. The probability of selecting an extra-large helmet is the ratio of extra-large helmets to the total inventory, which is

\frac{16}{120}

. Simplifying this fraction by dividing both the numerator and the denominator by their greatest common divisor (

8

) yields the final probability of

\frac{2}{15}

Step-by-Step Solution

Calculate the total number of known helmets.

45 + 35 + 24 = 104

To find the number of extra-large helmets, we first need to determine how many helmets belong to the other given size categories.

Determine the number of extra-large helmets.

120 - 104 = 16

Subtracting the sum of the known sizes from the total number of helmets gives the remaining count, which represents the extra-large helmets.

Set up the probability fraction.

\frac{16}{120}

The probability of a single event is the number of favorable outcomes (

16

extra-large helmets) divided by the total number of possible outcomes (

120

total helmets).

Simplify the fraction.

\frac{2}{15}

Divide the numerator and denominator by their greatest common divisor, which is

8

(

16 \div 8 = 2

and

120 \div 8 = 15

Key Concept

Single Event Probability

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