# Probability: A guide to acquiring wealth through Baba Ijebu Lotto.

This was my reaction when I discovered I had to study probability in my second week as a Mentee in She Code Africa Data Science Mentorship Program. I knew it was an important aspect of Data Science but I wasn’t in the mood for the random formulas I used when I studied it in school so I was a bit sceptical.

First thing on Sunday morning, Mr Israel Aminu, the mentor assigned to me, sent all resources I needed to study for the week. I was motivated by the fact that the course I needed to complete was part of the curriculum I currently use to study Data Science on Dataquest. I’ll be sharing the fundamental knowledge I acquired and I hope it’ll stop you from rolling your eyes the next time you hear anything about probability.

Probability is not about the odds, but about the belief in the existence of an alternative outcome, cause, or motive. — Nassim Nicholas Taleb

Wealth acquisition just like any other thing in life has a level of chances attached to it, factors such as luck and privilege cannot be overlooked.

Baba Ijebu, also known as Premier Lotto, is a popular gambling enterprise founded by Sir Kensington Adebutu, a businessman, socialite and a philanthropist. The game is popular among low-income earners in Nigeria due to its affordability (with just N20, one can get a stake in a game) and the availability of an offline gambling option.

The main principle of the game is to choose a specific five-digit number from 1 to 90. There are five variations of the game: Permutation, 2 Sure, 3 Direct, 4 Direct and 5 Direct. Permutation is a way of playing the Baba Ijebu lotto that guarantees a greater chance of winning. You can combine up to 10 numbers and if 2 out of your 10 chosen combined numbers comes out of the draw, you win a prize. The higher you stake, the greater the amount you win. 2 Sure allows you to predict 2 numbers out of the 5 drawn numbers. 3 Direct implies 3 predicted numbers and so on.

To calculate the probability of someone winning a Baba Ijebu game we will need to define some terms used in probability — no boring stuff, trust me :)

# Probability Notation, Rules and Terminologies

## Experiment

An experiment or trial is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes.

## Sample Space

A sample space is a set of all possible outcomes. It is often denoted by the capital Greek letter Ω(omega). The sample space for our Baba Ijebu game is {1,2,3,4,5,6,7,8,9,……..,90}

## Event

An event is a set of outcomes of an experiment(a subset of the sample space) to which a probability is assigned. An event can be Independent, Dependent or Mutually Exclusive. Independent events don’t influence each other’s probability. Dependent events influence each other’s probability. Mutually Exclusive events can not exist at the same time. You are either alive or dead, not both.

## Probabilities of Events

The probability of an impossible event is zero. The probability of a certain event is one and the probability of any event ranges between 0 and 1.

## Empirical and Theoretical Probability

Empirical Probability involves calculating the probability of an event by performing an experiment one or more times. Theoretical Probability involves calculating the probability of an event under the assumption that the outcomes have equal chances of occurring. Since we are broke and we are trying to acquire wealth, it doesn’t make sense to use empirical probability to predict our chance of winning a Baba Ijebu game.

## Sampling with(out) Replacement

To perform an experiment, you can either sample with or without replacement. Sampling with replacement is possible with independent events. Baba Ijebu game is sampled without replacement. If a number is pulled out of the sample space, the number of outcomes in the set decreases by one. This ensures that the Baba Ijebu number is unique, if you and your friend play a Baba Ijebu game together and your friend wins, you’ll go home empty-handed :(

## Union (OR)

For two events E and K, the union of the outcomes of these two events is a set. A set can only contain unique elements so the resulting set cannot include the elements that occur in both E and K more than one time. The Union operation is denoted by U.

## Intersection(AND)

This operation returns the unique element(s) between two or more events. It is denoted by n.

## The Multiplication Rule

The multiplication rule says:

For two events E and K, the probability that both events E and K happen can be found by multiplying the probability of E by the probability of K.

P(E n K) = P(E) * P(K).

Where P(E) and P(K) are probabilities of events E and K respectively.

Now let’s look into the chances of us winning Baba Ijebu game, shall we?

After a thorough look at our finances for the month, we concluded to play a 2 Sure. Recap: The main principle of the game is to choose a specific five-digit number from 1 to 90. A 2 Sure involves predicting 2 numbers out of the 5 Baba Ijebu number. Another important thing you need to remember is that Baba Ijebu is sampled without replacement.

Let the first number be an event E and the other number be K. The probability of event E is P(E) and the probability of event K is P(K).

The Sample space for Baba Ijebu, Ω = {1,2,3,4,5,6,7,8,9,……..,90}

P(E) = 1/90 and P(K) = 1/89

Using the multiplication rule:

P(E n K) = P(E) * P(K) = (1/90) * (1/89) = 1/8010 = 0.00012484395

I’m trying not to laugh, but really that’s the probability of you successfully predicting two of the 5 Baba Ijebu numbers :)

Now imagine predicting all 5 numbers correctly.

LMAO. Go and work, lazy bone.