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Difficulty: EasySingle Event Probability

A supply room bin contains a mixture of 3030 electronic components. There are 1212 resistors, 1010 capacitors, and 88 inductors. If a technician randomly selects one component from the bin, what is the probability that the selected component is an inductor?

  1. 415\frac{4}{15}Answer
  2. B
    411\frac{4}{11}
  3. C
    1115\frac{11}{15}
  4. D
    154\frac{15}{4}

Answer

The probability of selecting an inductor is 415\frac{4}{15}.
The correct probability is found by dividing the number of inductors (88) by the total number of components (3030). This gives the fraction 830\frac{8}{30}, which simplifies to 415\frac{4}{15} by dividing both the numerator and the denominator by their greatest common factor, 22.

Step-by-Step Solution

1
Identify the total number of possible outcomes.
Total components = 3030
The denominator for single event probability is always the total number of items available.
2
Identify the number of favorable outcomes.
Number of inductors = 88
The numerator represents the specific event being measured (selecting an inductor).
3
Set up the probability fraction and simplify.
Probability = 830=415\frac{8}{30} = \frac{4}{15}
Probability is favorable outcomes over total outcomes, and the resulting fraction must be reduced to its simplest form.

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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