Introduction to Probability

We use words like chance or uncertainties in our day-to-day life. For example, there is a chance that India may win or lose the World Cup; there is a chance of getting head or tail whenever we toss a coin, etc. These events are uncertain. Some situations in our life are certain to happen as the sun will always rise in the east. Some of the situations may be impossible to happen, like, the sun will never rise from the west. This type of situation that may or may not happen indicates probability. The words chance and probability can actually be expressed mathematically. 

So what is probability?

Probability means something that may happen but is uncertain. The definition has been given by a French mathematician named Laplace. Probability can simply be satopicId to be the chance of something happening or not happening.

For example: The sun will set on the east stopicIde. The probability of this will be zero. As the sun always sets on the west stopicIde, not from the east stopicIde. 

Certain rules of probability:

The probability of the event lies between zero and one. If there is no chance of happening then the probability will be zero and for those that are bound to happen then the probability will be one. It was pioneered in 18 century that illustrates the probability involving games of chance like throwing the coin, dice, pulling out, etc. 

Definition of probability

A probability is a figure that demonstrates the chance or odds that a specific event will take place. It lies between zero and one. The higher the probability of an event the more likely it is that the event will occur.

Formula of probability:

P(E) = Number of expected outcomes/ total number of outcomes. 

Here, P(E) denotes the probability that an event will take place.

Example 1: what is the probability of getting head when a coin is tossed? 

 When a coin is tossed we can get either heads or tails ( H , T) 

The probability of getting head will be

P(E) = Number of favourable outcomes /total number of outcomes

         = 1/ 2 

So the probability of getting head when a coin is tossed will be 1 /2 

Example 2:  There are two Rose flowers, 5 Lotus flowers, and three Lilly flowers in a basket. What is the probability of getting lily flowers? 

Total number of outcomes will be ( 2+5+3) = 10 flowers 

So the number of favourable outcomes that is getting the lily flower is 3 

P(E) = Number of favourable outcomes/ total number of outcomes

         = 3/10

So the probability of getting a lily flowers is 3/10 

Example 3: Random card is selected from a pack of cards. What is the probability that the card drawn is Ace card?

A pack of cards contains 52 cards. ( total outcomes) 

Let A be the event where the probability of getting an ace card. 

Total number of ace cards= 4

P(A) = Number of favourable outcomes/ total number of outcome 

         = 4/52

         =1/13 ( after simplifying 4 upon 52)

Who is the probability of getting a Ace cards = 1/13