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17 Probability

The fundamental groundwork of probability was done by two French mathematicians Blaise Pascal
and Pierre de Fermat. It was first developed to understand the game of chance and betting involved
in it.

Blaise Pascal Pierre de Fermat
Let’s understand the concept of probability with the help of the following statements:

• If you throw a die, the number on top shall be less than 7.
• A square of greater side will have a larger area as compared to the square with smaller side.
The above two statements are certainly true. Each number on a die is less than 7 and obviously a
square having greater side is bigger, hence encloses a larger area.
In daily life we come across statements such as:

• Probably it will rain today.
• Getting head in a toss of a coin.
The first statement doesn’t guarantee rain. In fact no one can predict with certainty, whether it will
rain on a particular day or not. Similarly, if a coin is tossed once, the chances of getting a head
are equal to the chances of not getting it. Therefore, we say the chances of getting a head or not
getting it are even.
Finally consider events which are not possible:

• A green-coloured card drawn from a well-shuffled deck of playing cards
• A triangle in which the sum of measures of two sides is less than the third side
Since cards are either red or black, therefore drawing a green card is not possible. In a triangle
the sum of two sides is always greater than the third side. Therefore, a triangle in which the sum
of two sides is less than the third side is also not possible.

Probability
In the examples discussed above, we note that certain events are sure to happen, some events may
or may not occur and some are impossible. The events which may or may not occur might differ
from each other in their likelihood of occurrence. Let’s understand this by an example. Suppose