High School

There are 319,319 plastic chips numbered 1 through 319,319 in a box. What is the probability of reaching into the box and randomly drawing the chip numbered 181,181?

Express your answer as a simplified fraction or a decimal rounded to four decimal places.

Answer :

To find the probability of drawing the chip numbered 181181 from a box containing plastic chips numbered from 1 to 319319, we can follow these steps:

  1. Determine the Total Number of Chips: The chips are numbered consecutively from 1 to 319319. Therefore, there are a total of 319319 chips in the box.

  2. Determine the Number of Favorable Outcomes: The favorable outcome here is drawing the chip numbered 181181. There is exactly 1 chip with this number.

  3. Calculate the Probability: Probability is found by dividing the number of favorable outcomes by the total number of outcomes. In this case:

    [tex]\text{Probability} = \frac{1}{319319}[/tex]

    Calculate the decimal equivalent by dividing 1 by 319319:

    [tex]\text{Decimal Probability} \approx 0.0000031[/tex]

    This decimal should be rounded to four decimal places, giving:

    [tex]\text{Decimal Probability Rounded} \approx 0.0000[/tex]

Note that the decimal probability is very small, practically zero when rounded to four decimal places, indicating that the chance of drawing the chip numbered 181181 is very low.

Thus, the probability of drawing the chip numbered 181181 from this box is [tex]\frac{1}{319319}[/tex], or approximately 0.0000 when rounded to four decimal places.

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