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Difficulty: EasySingle Event Probability

A communications specialist is inventorying a batch of hand-held radios. The batch contains 1818 VHF radios, 1212 UHF radios, and 2020 dual-band radios. If one radio is randomly selected for a quality check, what is the probability that it is a VHF radio? Express your answer as a simplified fraction.

Answer: 9/25 / 9 / 25 / \frac{9}{25}

Answer

9/25
The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. There are 1818 VHF radios and a total of 5050 radios (18+12+2018 + 12 + 20). The probability is 1850\frac{18}{50}, which simplifies to 925\frac{9}{25} by dividing both the numerator and the denominator by 22.

Step-by-Step Solution

1
Calculate the total number of radios in the batch.
18+12+20=5018 + 12 + 20 = 50
The denominator of a probability fraction represents the total number of possible outcomes.
2
Identify the number of favorable outcomes.
1818 VHF radios
The numerator of a probability fraction represents the number of favorable outcomes.
3
Set up the probability ratio and simplify.
1850=925\frac{18}{50} = \frac{9}{25}
Probability is the ratio of favorable outcomes to total outcomes, and the question asks for a simplified fraction.

Key Concept

Single event probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
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Topics

Single Event Probability

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