Page 264 - ICSE Math 7

23 Probability

Key Concepts

• Probability • Experimental Probability
• Some Important Terms Used in 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.
Let’s understand the concept of probability with the help of
the following statements.
• If you throw a die, the number on its top shall be less
than 7. Blaise Pascal Pierre de Fermat
• 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
the statement “Probably it will rain today” is made during a rainy season, when it is raining almost
everyday. Then the chances of actually raining is greater than if the statement is made on a dry
sultry day in summer. Mathematically, it is equivalent to saying that the probability of rain on a
particular day can be high or low depending upon the weather. Now let’s give the formal definition
of probability.
Probability is defined as the measure of likelihood of the occurrence of an event.

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