How to Derive More Odds From a Given Three Fixed Odds

Mutually Exclusive Events

• 1

  Convert the odds into fractions that represent the number of favorable outcomes in the numerator and the total number of outcomes in the denominator.

  For example, a 1 in 100 chance of pulling out a gold coin can be represented as 1/100, making the silver coin 5/100, and copper coin: 1/10.

• 2

  Add the fractions together to determine the likelihood that one of two or more mutually exclusive events will occur. For example, pulling out one of the special coins.

  1/100 + 5/100 + 1/10 = 16/100

• 3

  Reduce the fraction to its lowest terms. This is the probability that one of the events will occur.

  For example, the odds of pulling out one of the special coins are 4/25, or 4 out of 25.

Independent Compound Events

• 4

  Convert the odds into fractions.

• 5

  Multiply the fractions to determine the odds of all three events occurring, if one does not impact the probability of the other.

  For example, if each child were given three chances to draw a coin, and each time he drew, the previous coin was placed back into the jar, there would be no change in the probability of drawing a special coin the second or third time. Therefore the probability of drawing a gold, silver and copper coin is 1/100 * 5/100 * 1/10 = 5/100,000.

• 6

  Reduce the fraction to its lowest terms. This is the probability that both of the events will occur.

  The odds of drawing a gold and silver is 1/20,000, or 1 in 20,000.

Dependent Compound Events

• 7

  Convert the odds of the first event into a fraction.

  For example, the odds of drawing a copper coin are 1/10.

• 8

  Change the odds of the second event to reflect the smaller number of possible outcomes.

  For example, if each child got three chances to draw a coin, but did not put the coin back into the jar before drawing again, the number of possible coins he could draw the second time would be one less than the first time. Therefore, instead of the odds of drawing a silver coin being 2/100, they would be 2/99.

• 9

  Change the odds of the third event to reflect the smaller number of possible outcomes.

  Once the child has drawn two coins, there is now a 1/98 chance of drawing the gold coin.

• 10

  Multiply the fractions to determine the probability that all three events will occur.

  1/10 * 2/99 * 1/98 = 2/97,020.

• 11

  Reduce the fraction to its lowest form.

  The probability of drawing a copper coin, followed by a silver coin, followed by a gold coin is 1/48,510.