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Difficulty: MediumSingle Event Probability

An electrician's toolbox contains 88 red wire connectors, 1414 blue wire connectors, and 1010 green wire connectors. If the electrician randomly selects one connector without looking, what is the probability that it is NOT a blue connector?

  1. 916\frac{9}{16}Answer
  2. B
    716\frac{7}{16}
  3. C
    79\frac{7}{9}
  4. D
    516\frac{5}{16}

Answer

916\frac{9}{16}
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. There are 32 total connectors in the toolbox. The number of connectors that are NOT blue is 18 (8 red + 10 green). Therefore, the probability is 18/32, which simplifies to 9/16.

Step-by-Step Solution

1
Calculate the total number of wire connectors in the toolbox.
8+14+10=328 + 14 + 10 = 32 total connectors.
The denominator of a probability fraction represents the total number of possible outcomes.
2
Determine the number of favorable outcomes (connectors that are NOT blue).
88 (red) +10+ 10 (green) =18= 18 connectors that are not blue. Alternatively, 3232 (total) −14- 14 (blue) =18= 18.
The question asks for the probability of selecting a connector that is NOT blue.
3
Set up the probability fraction and simplify.
1832=18÷232÷2=916\frac{18}{32} = \frac{18 \div 2}{32 \div 2} = \frac{9}{16}
Probability is favorable outcomes over total outcomes, and must always be expressed in simplest form.

Key Concept

Single Event Probability
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Topics

Single Event Probability

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