The solution to this question is simple but complex….

There is a 1 in 10 chance the ‘Go Live’ date will be delayed by Project 1

There is a 1 in 10 chance the ‘Go Live’ date will be delayed by Project 2

There is a 2 in 10 chance the ‘Go Live’ date will be delayed by Project 3

What is the probability of going live on March 1st?

To understand this problem let’s look at the role of dice:

If role the dice and get a 1 the project is delayed, any other number it is on time or early.

If you role 1 dice, the probability is 1 in 6 it will land on 1 = 0.1666 or 16.66% therefore there is a 100 – 16.66 = 83.34% probability of success.

Similarly, if you roll 2 dice, there are 36 possible combinations, and the possibilities of losing are: 1:1, 1:2, 1:3, 1:4, 1:5, 1:6, 6:1, 5:1, 4:1, 3:1, 2:1. (11 possibilities)

The way this is calculated (in preference to using the graphic) is to take the number of ways a single die will NOT show a 1 when rolled (five) and multiply this by the number of ways the second die will NOT show a 1 when rolled. (Also five.) 5 x 5 = 25. Subtract this from the total number of ways two dice can appear (36) and we have our answer…eleven.

(source: http://www.edcollins.com/backgammon/diceprob.htm)

Therefore the probability of rolling a 1 and being late are 11/36 = 0.3055 or 30.55%, therefore the probability of success is 100 – 30.55 = 69.45% probability of being on time.

If we roll 3 dice we can extend the calculation above as follows:

The number of possible outcomes are 6 x 6 x 6 = 216

The number of ways not to show a 1 are 5 x 5 x 5 = 125

Meaning there are 216 combinations and there are 125 ways of NOT rolling a 1

leaving 216 – 125 = 91 possibilities of rolling a 1

(or you can do it the hard way: 1:1:1, 1:1:2, 1:1:3, etc.)

91/216 = 0.4213 or 42.13% probability of failure therefore there is a

100 – 42.13 = 57.87% probability of success.

So going back to the original problem:

Project 1 has a 1 in 10 chance of causing a delay

Project 2 has a 1 in 10 chance of causing a delay

Project 3 has a 1 in 5 chance of causing a delay

There are 10 x 10 x 5 = 500 possible outcomes and within this 9 x 9 x 4 = 324 ways of not being late. 500 – 324 leaves 176 ways of being late. 176/500 = 0.352 or a 35.2% probability of not making the ‘Go Live’ date.

Or a 100 – 35.2 = 64.8% probability of being on time.

The quicker way to calculate this is simply to multiply the probabilities together:

0.9 x 0.9 x 0.8 = 64.8%

These calculations have been added to our White Paper on * Probability*.