Page 304 - Start Up Mathematics_7
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(d) Since each number on the die is less than 7
6
∴ P (number less than 7) = = 1
6
(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. For example, tossing a coin, throwing a die, etc.
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 coin is tossed once. The sample space consists of outcomes: H, T
(b) A 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.
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