How to Calculate Joint Probability

Rolling dice multiple times consitutes independent events.

Joint probability refers to the chances that two independent events occur. Examples of independent events are two different coin tosses or two different rolls of the dice; the first outcome does not affect the second. However, drawing cards from a deck without replacing the drawn card are not independent events because each time a card is drawn, it affects the probability of the next card. To figure joint probability, you first have to figure the probability of each of the independent events.

Things You'll Need

• Calculator

Instructions

1. Calculate the probability of the first event happening by dividing the number of successful results by the total possible results. For example, if you want to roll a 4 when you roll two dice, there are three ways -- (1,3), (2,2) and (3,1) -- and 36 total possible outcomes. Therefore, the probability would be 4/36, or 0.1111.

2. Calculate the probability of each other event for which you want to calculate the joint probability. For example, if you want to find the joint probability of rolling a 4 and then rolling a 10, 11 or 12 on the next roll, you would calculate the probability of rolling 10, 11 or 12 by dividing the number of ways to roll one of those numbers, six, and the total number of possible outcomes, 36, to get 6/36, or 0.1667.

3. Multiply the probability of each independent outcome occurring by each other to find the joint probability. In this example, multiply 1/9 by 1/6 to get 1/54, or about 0.0185, or about 1.85 percent.

References

• UC Riverside: What are the Chances?
• University of Vermont: Hypothesis Testing and Probability; David C. Howell; 2001