A motor pool inventory shows that \frac{1}{4} of the vehicles are heavy trucks, \frac{1}{3… — Armed Services Vocational Aptitude Battery (ASVAB)

A motor pool inventory shows that $\frac{1}{4}$ of the vehicles are heavy trucks, $\frac{1}{3}$ are light tactical vehicles, and the remaining vehicles are armored personnel carriers. If a vehicle is randomly selected for an inspection, what is the probability that it is an armored personnel carrier?

A
$\frac{7}{12}$
B
$\frac{2}{7}$
$\frac{5}{12}$ Answer
D
$\frac{5}{7}$

Answer

\frac{5}{12}

The total probability of all mutually exclusive events must sum to 1. First, find the combined probability of heavy trucks and light tactical vehicles by using a common denominator of 12:

\frac{1}{4}

becomes

\frac{3}{12}

and

\frac{1}{3}

becomes

\frac{4}{12}

. Their sum is

\frac{7}{12}

. Since the remaining vehicles are armored personnel carriers, subtract this sum from the total probability of 1 (or

\frac{12}{12}

). The result is

\frac{5}{12}

Step-by-Step Solution

Find the combined probability of selecting a heavy truck or a light tactical vehicle.

\frac{1}{4} + \frac{1}{3}

To determine the portion of the fleet that is not armored personnel carriers, the given fractions must be added.

Add the fractions by finding a common denominator.

\frac{3}{12} + \frac{4}{12} = \frac{7}{12}

Fractions must have the same denominator (12) before their numerators can be added.

Subtract the combined fraction from 1 (the total probability).

1 - \frac{7}{12} = \frac{12}{12} - \frac{7}{12} = \frac{5}{12}

The sum of probabilities for all possible events must equal exactly 1. The remainder represents the armored personnel carriers.

Key Concept

Single Event Probability from Complementary Events

Estimated Time:1m 0s

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