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Simple probability, step by step

The probability of one event is how many ways it can happen over how many ways anything can.

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The question

4 red, 4 blue, 4 green — P(blue)

4 + 4 + 4=12
4 + 4 + 4=12
blue:4
4 + 4 + 4=12
blue:4
4 + 4 + 4=12
=
  1. Count EVERYTHING first, before the ones being asked about: 4 + 4 + 4 = 12 altogether. That is the bottom of the fraction, and it is the half that gets swapped for the wrong number.
  2. Now the ones that count as a win: 4 blue.
  3. Chance is the wins OVER the total — not over the rest. So it is 4 out of 12.
  4. And 4/12 can be written in bigger pieces: 1/3.

How it works.

  1. 01

    Count EVERYTHING first, before the ones being asked about: 4 + 4 + 4 = 12 altogether. That is the bottom of the fraction, and it is the half that gets swapped for the wrong number.

  2. 02

    Now the ones that count as a win: 4 blue.

  3. 03

    Chance is the wins OVER the total — not over the rest. So it is 4 out of 12.

  4. 04

    And 4/12 can be written in bigger pieces: 1/3.

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