Calculating Cumulative Probability

Probability is the measure of the possibility that a given event will occur. Cumulative probability is the measure of the chance that two or more events will happen. Usually, this consists of events in a sequence, such as flipping “heads” twice in a row on a coin toss, but the events may also be concurrent. The only restriction is that each event must be independent of the other and have probability that it could occur by itself.

Step 1

Calculate the probability of the first event occurring. Six different outcomes are possible for the roll of a die, and each number can only occur once per roll. Therefore, the probability of rolling a “1” is one in six, or 0.167

Step 2

Calculate the probability of the second event occurring. The probability of rolling a “2” is still 0.167. By comparison, the probability of rolling an even number is three in six, or 0.5, since there are three even numbers on the six faces.

Step 3

Continue this process until you have calculated the individual probabilities for each independent event.

Step 4

Multiply the probabilities together to determine the cumulative probability. For example, the probability of rolling three 2s in a row is: (0.167)(0.167)(0.167) = 0.0046 or 1/216 The probability of rolling an odd number followed by an even number is: (0.5)(0.5) = 0.25

Warning

You cannot use this method to solve problems like calculating the probability of rolling a 7 or 11 with two separate rolls. For example, a 7 can be a 1-6, 2-5 or 3-4 combination. If the first die is a 5, then the second has to be a 2. Therefore, the two events are not independent. In this case, the two dice are one set, and you must calculate the probability accordingly.

References

• Advanced Engineering Mathematics, 7th ed.; Erwin Kreyszig; 1993