Page 303 - Start Up Mathematics_7

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.
Suppose Divya, Garima, Rohit, Ravi and Arman are the 5 finalists out of which only 1 is to be
selected to represent the school in a competition. Each one of them has the same chance of being
selected. The probability of Divya being selected is 1 event out of 5 possible outcomes. Therefore,
1 1
the probability of Divya’s selection is and is represented by P(Divya). The fraction implies there
5 5
is 1 chance of Divya’s selection out of a total of 5. Similarly probability of a boy being selected
3
to represent the school is denoted by P(Boy) and is . The selection of Divya or a boy are events
5
and the whole process of selection out of 5 students is an experiment. Thus, probability can be
considered a fraction expressing how many times an event will occur in a given number of times.
The probability of an event E denoted by P(E) is given by:

P (E) = Number of outcomes in which E occurs
Total number of outcomes
Let’s try to understand the concept of probability using examples which result in outcomes having
equal chances of occurrence.
Example 1: A coin is tossed once. What is the probability of getting a head?
Solution: There are 2 possible outcomes, either head or tail. There is only one outcome which
is favourable. Hence, if we denote probability of head by P(H), then:

P (H) = Favourable outcomes = 1
Total outcomes 2
Example 2: A die is thrown once. Find the probability of getting the following numbers on the
die:

(a) P (1) (b) P (even number) (c) P (prime number)
(d) P (number less than 7) (e) P (number greater than 6)
Solution: We know a die has six faces with equal chances of the numbers 1, 2, 3, 4, 5 or 6

coming on top.
(a) Since 1 is the only favourable outcome
1
∴ P (1) =
6
(b) We have three even numbers, i.e., 2, 4 and 6
3 1
∴ P (even number) = =
6 2
(c) Since favourable outcomes are prime numbers, i.e., 2, 3 and 5
3 1
∴ P (prime number) = =
6 2

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