# Betting probability – part 3 – Rules of Multiplication

Betting probability is being grinded down, one article at a time here on Howtobet.net. The scope of this article is to show you how the rules of multiplication work out. Those two betting probability rules are the special rule of multiplication and the general rule of multiplication.

You will learn how to define the joint probability of two events using the multiplication rule. You will learn how to differentiate between dependent and independent variables. Finally, you will learn how to master how to calculate the joint probability of any number of independent events.

## The special rule of multiplication

We need to make you aware that we here will be looking at independent events and dependent events separately.

### Independent events

In betting probability the special rule of multiplication requires that two events, A and B are independent. You know two events are independent if the occurrence of one event doesn’t have any effect on the probability of the other event. If we want to find the probability for independent events happening, we multiply the probabilities with each other.

#### Example of independent event

An example of this would be flipping a fair coin twice. Using logic we deduce that it is 50% chance for each of the two possible outcomes, and that a previous outcome doesn’t affect the next outcome of this coin flipping experiment.

In our betting probability example with two coin flips, let’s see what the probability for two heads in a row is: The denotation in probability theory would be P (A and B), P meaning probability, A and B meaning each of the coin flipping events. To drill it home: Probability of (Heads on flip 1 and Heads on flip 2).

As we mentioned above, we simply multiply the probabilities and get P= chance of heads flip 1 x chance of heads flip 2 = 0.5%x0.5% = 0.25 = 25% chance of seeing two heads in a row.

#### Quick look at variants of independent events

Just to make sure you know this too: You use the same multiplication rule to find probability no matter how many events you deal with as long as they are independent. These events may also have different probabilities attached. They do not need to be of the same probability as our example was.

### Dependent events

The betting probability plot is thickening. Dependent events refers to that occurrence of one event has an effect on the probability of the other event or set of events.

#### Here is an example for you

Say you own a value bet screening software that monitors the betting market and has a success rate of 80% finding value of 5%+. You have found 25 bets that match your bet analysis criteria. One bet is selected from this group for manual bet analysis and quality check. At this point in time it is 5/25 = 1/5 = 20% chance it doesn’t pass as a value bet upon further bet analysis. Let’s for argument sake assume it doesn’t match the manual value bet criteria’s. The next potential value bet out now has a probability of 4/24 = 1/6 = 16.67% being a dud as well. The next bet has a 5/6 or 83,33% chance of actually being the real deal.

Conditional probability is used to generalize the rule of multiplication.

## The general rule of multiplication

The general rule of multiplication is used to find the joint probability that two events will occur one after another.

The formula used is denoted like this: P (A and B) = P (A) x P (B|A) or P (A and B) = P (B) x P (A|B). You can view this as the probability of event A and B happening = the probability of A happening x the probability of B happening *given that A happened* or; the probability of event A and B happening = the probability of B happening x the probability of A happening *given that B happened.*

### Example

Let’s stay with the value bet screener example from above. What is the probability of both the two first bets selected from the 25 bets basket isn’t value after all?

Let event A be the probability of the first bet not being value after all; P (A) = 5/25. Let B be the probability of the bet selected as number two not be value either; P (B) = 4/24.

If you wonder why B is 4/24; it is because the first bet wasn’t value so there aren’t 5 bad value bets left in the selection, and you have picked one out of the total 25 bet basket, so there is only 24 bets left.

Now, let’s man up and denominate this like the professionals. P (A and B) = P (A) x P (B|A) = 5/25 x 4/24 = 200/600 = 0.0333 = 3.33%. So, the chance of both first bets out of the 25 bet basket being no go betting wise is a meager 3.33%.

You really should work through this example yourself and preferably also work out some similar examples just to get the hang of it. You should also add events to the examples. You can use our formula for three and more events.

Just to show you; for three events the formula would look like this: P (A and B and C) = P (A) x P (B|A) x P (C|A and B). Using the value bet screener example above this would end up being 5/25 x 4/24 x 3/23 = 60/13800 = 0.0043 = 0.43%

## Rounding it off

This article has already gotten way to long, sorry! In the next article we look at rules of addition and the total probability rule.

We suggest you read our other articles on probability. They are found here:

- betting probability introduction
- Unconditional, conditional and joint betting probability

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