# Classical probability

#### Math Formulas

## Classical probability

**Definition :-**Probability is the mathematical study of measuring uncertainty. Probabilities are classically determined when their numerical values are based upon an enumeration of every possible outcome.

**Mathematical description :-**Probability is a type of ratio where we compare how many times an outcome can occur compared to all possible outcomes.

**Real Life Application :-**Before planning for an outing or a picnic, we always check the weather forecast. Suppose it says that there is a 60% chance that rain may occur. Do you ever wonder from where this 60% come from? Meteorologists use a specific tool and technique to predict the weather forecast. They look at all the other historical database of the days, which have similar characteristics of temperature, humidity, and pressure, etc. And determine that on 60 out of 100 similar days in the past, it had rained.

**Example 1 :-**What is the probability of drawing a king and a queen consecutively from a deck of 52 cards, without replacement.

**Solution :-**

Probability of drawing a king = 4/52 = 1/13

After drawing one card, the number of cards are 51.

Probability of drawing a queen = 4/51.

Now, the probability of drawing a king and queen consecutively is 1/13 * 4/51 = 4/663

**Example 2 :-**Consider an example where a pack contains 4 blue, 2 red and 3 black pens. If a pen is drawn at random from the pack, replaced and the process repeated 2 more times, What is the probability of drawing 2 blue pens and 1 black pen?

**Solution :-**

Here, total number of pens = 9

Probability of drawing 1 blue pen = 4/9

Probability of drawing another blue pen = 4/9

Probability of drawing 1 black pen = 3/9

Probability of drawing 2 blue pens and 1 black pen = 4/9 * 4/9 * 3/9 = 48/729 = 16/243