Page 266 - ICSE Math 7

(e) Since no number on the die is greater than 6

0
∴ P (number greater than 6) = = 0
6
Example 3: A box contains 5 red and 7 white marbles. A marble is drawn at random from the box.
Find the probability that it will be a:
(a) red marble (b) white marble
5 5 7 7
Solution: (a) P (red marble) = = (b) P (white marble) = =
5 + 7 12 5 + 7 12

From these examples, we conclude that probability ‘p’ of an event is a number greater than or equal to
0 and less than or equal to 1, i.e., 0 ≤ p ≤ 1. Events that have no chance of happening have probability
0 and events which are sure to happen have probability 1. For other events depending on their chances
of occurrence the probability lies between 0 and 1.

Some Important Terms Used in Probability

1. Random Experiment: An experiment whose all possible outcomes are known but the exact
outcome cannot be predicted. Example: tossing a coin and throwing a die.
2. Trial: Each time we perform an experiment, it is called a trial.
3. Sample Space: A sample space is a list of all possible outcomes of an experiment. Let’s consider
some examples.
(a) A fair coin is tossed once. The sample space consists of outcomes: H, T

(b) A fair coin is tossed twice. The sample space consists of outcomes: HH, HT, TH, TT
(c) If two dice are thrown together, then the sample space consists of following outcomes:
(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)
(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)
(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)
(d) In a cricket match between India and England, the outcomes are: India wins, India loses or
a tie.

4. Event: A part or whole of a sample space is called an event. For example, getting a head in a toss
of a coin or getting a doublet in a throw of a pair of dice, i.e., (1, 1), (2, 2), (3, 3), (4, 4), (5, 5),
(6,6) constitutes an event.

Experimental Probability
When a probability is determined by observing the outcomes of an experiment, it is said to be determined
experimentally or empirically. For example, Shreya tossed a coin 10 times and she tabulated the
result as follows:

Head 7
Tail 3

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