Page 112 - Math_Genius_V1.0_C8_Flipbook

E:\Working\Focus_Learning\Math_Genius-8\Open_Files\05_Chapter_4\Chapter_4
\ 06-Jan-2025 Bharat Arora Proof-6 Reader’s Sign _______________________ Date __________

( f) Impossible Event: An impossible event is an event with no chance of occurring. If a coin
is tossed, then the possible occurrence will be either tails or heads. We cannot expect
both tails and heads to occur simultaneously. Thus, getting both heads and tails while
tossing a coin is an impossible event.
( g) Sample Space: The collection of all possible Remember
outcomes of an experiment is called Tossing a Tossing Tossing
its sample space. It is denoted by S. For single coin two coins three coins
example, simultaneously simultaneously
( i) In tossing a coin, S = {H, T} \ n(S) = 2 H H (HHH)
T(HHT)
( ii) In tossing a pair of coins or a single (H) (HH) H (HTH)
T
coin twice, simultaneously (HT) T(HTT)
H (THT)
S = {HH, HT, TH, TT} \ n(S) = 4 H T(TTH)
(T) (TH) H (TTH)
( iii) In tossing three coins simultaneously or T
a single coin thrice, (TT) T(TTT)

S = {HHH, HHT, HTH, THH, TTH, THT, Elementary outcomes
HTT, TTT} \ n(S) = 8
( iv) In rolling a die, S = {1, 2, 3, 4, 5, 6}

\ n(S) = 6
( v) In rolling a pair of dice simultaneously or a single die twice,
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

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

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

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} \ n(S) = 36

Quick Check

Classify the following statements under appropriate headings.
(a) Getting the sum of angles of a triangle as 180°. (b) India winning a cricket match
(c) Sun setting in the evening. (d) Getting 7 when a die is thrown.
(e) Sun rising from the west. (f) Winning a racing competition by you.
Certain to happen Impossible to happen May or may not happen

Favourable Events

An event which contains an element of sample space is called a favourable event. It is also called
a successful event. The outcomes which ensure the occurrence of an event are called favourable
outcomes of that event and the remaining outcomes are called unfavourable outcomes of that
event.

Mathematics-8 110