How to Combine Probability Distributions

A probability distribution is a visual representation of the values a variable can assume, with their corresponding probabilities. If the values for the variable are discrete, then the probability distribution can be either a table or a graph of the probabilities. If the values are continuous, then the distribution will be a curve showing the probabilities for values of the variable. The probability for each potential value will be greater than zero and less than one, and the sum of the probabilities will equal one. A joint probability distribution is the representation of the simultaneous behavior of two variables. If the two variables are independent, the probability of the combined values for each variable will equal the probability of one value times the product of the other value.

Things You'll Need

  • Calculator
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Instructions

    • 1

      Set up a table in which the values for one variable are displayed across the top of the table, and the values for the other variable are displayed to the left of the table. For example, if you were looking at the probabilities that a frog was green or brown, and preferred to eat crickets, moths, or mealworms, then you would list the two colors along the left side of the table and the three foods along the top of the table.

    • 2

      Insert the probabilities for each value along the side of the table opposite where the values of the variable are listed. If the probability that the frog is green is 70 percent and the probability that it is brown is 30 percent, then write 0.7 on the right side of the table directly opposite the word green, and 0.3 on the right side of the table opposite the word brown. If the probability that a frog showed a preference toward crickets, moths, or mealworms is 40 percent, 35 percent, and 25 percent respectively, then write 0.4, 0.35, and 0.25 under the graph beneath the corresponding food.

    • 3

      Multiply the probability of each value for one variable times the probability of each value for the other value, and write the product of the two probabilities into the intersecting box of the table. Since 70 percent of the frogs are green and 40 percent prefer to eat crickets, multiply the two probabilities together and write 0.28 at the intersection of green and cricket. The other probabilities in this example should be 0.245, 0.175, 0.12, 0.105, and 0.075.

    • 4

      Add the probabilities of each intersecting box of the table together. If the computations have been done correctly, the sum of the joint probabilities should equal one.

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