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Zorluk: KolaySingle Event Probability

An intelligence analyst has a container of map pins used for marking locations on a briefing board. The container holds 2424 red pins, 1616 blue pins, and 1010 green pins. If the analyst randomly selects one pin from the container, what is the probability that it is a blue pin?

  1. 825\frac{8}{25}Cevap
  2. B
    817\frac{8}{17}
  3. C
    1225\frac{12}{25}
  4. D
    23\frac{2}{3}

Cevap

The probability of selecting a blue pin is 825\frac{8}{25}.
The probability of a single event is found by dividing the number of favorable outcomes by the total number of outcomes. There are 1616 blue pins (favorable outcomes) and a total of 5050 pins (24+16+1024 + 16 + 10). This creates the fraction 1650\frac{16}{50}, which simplifies to 825\frac{8}{25} when both numbers are divided by 22.

Adım Adım Çözüm

1
Determine the total number of possible outcomes.
24 (red)+16 (blue)+10 (green)=50 total pins24 \text{ (red)} + 16 \text{ (blue)} + 10 \text{ (green)} = 50 \text{ total pins}
The denominator of a probability fraction must represent all possible items that can be selected.
2
Identify the number of favorable outcomes.
16 blue pins16 \text{ blue pins}
The numerator must represent the specific event being asked for (selecting a blue pin).
3
Set up the probability fraction and simplify.
1650=16÷250÷2=825\frac{16}{50} = \frac{16 \div 2}{50 \div 2} = \frac{8}{25}
Fractions must always be reduced to their simplest form by dividing both the numerator and denominator by their greatest common factor.

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