**Definition of Theoretical Probability**

Probability is a likelihood that an event will happen.

We can find the theoretical probability of an event using the following ratio:

Let’s do a couple of examples.

**Solution:**

Tossing a tail is the favorable outcome here.

When you toss a coin there are only 2 possible outcomes: a Head or a Tail

So the options for tossing a tail are 1 out of 2.

We can also represent probability as a decimal or as a percent.

**Example 2**

**A bag contains 20 marbles. 15 of them are red and 5 of them are blue in color. Find the probability of picking a red marble.**

Let’s first answer a few questions here:

If I am going to randomly pick a marble from the bag then what results can I have:

I’ll either pick a red marble or a blue one.

My next question is what the chances of picking a red marble are:

There are 15 red marbles and just 5 blue marbles.

It’s obvious that we have three times as many red marbles as blue marbles.

So, the chance of picking a red marble is more than that of the blue one.

Therefore, the probability of picking a red marble is:

**Find the probability of getting a sum of 7 when you roll two dice.**

Two dice are being rolled. The possible outcomes are as follows:

Let’s use the representation (a, b) for the outcomes where **a = number on dice 1** and **b = number on dice 2**.

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

There are 36 possible outcomes in all.

**The question is when you roll two dice, what are the chances of getting a sum of 7?**

From the list above identify the pairs with outcomes that add up to 7.

Let’s highlight them this way:

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), **(1, 6),**

(2, 1), (2, 2), (2, 3), (2, 4), **(2, 5),** (2, 6),

(3, 1), (3, 2), (3, 3), **(3, 4),** (3, 5), (3, 6),

(4, 1), (4, 2), **(4, 3)**, (4, 4), (4, 5), (4, 6),

(5, 1), **(5, 2)**, (5, 3), (5, 4), (5, 5), (5, 6),

**(6, 1)**, (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Observe that the pairs along the main diagonal add up to 7. There are 6 such pairs.

So, the probability of getting a sum of 7 when we roll two dice is:

- Probability
- Event
- Outcome
- Ratio