Three coins are tossed. Describe two events which are mutually exclusive but not exhaustive.
(N/A) When three coins are tossed,the sample space $S$ is given by:
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Two events which are mutually exclusive but not exhaustive can be defined as:
$A$: Getting exactly one head.
$B$: Getting exactly one tail.
Here,the sets are:
$A = \{HTT, THT, TTH\}$
$B = \{HHT, HTH, THH\}$
These events are mutually exclusive because $A \cap B = \phi$.
They are not exhaustive because $A \cup B = \{HTT, THT, TTH, HHT, HTH, THH\} \neq S$.
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Two events which are mutually exclusive but not exhaustive can be defined as:
$A$: Getting exactly one head.
$B$: Getting exactly one tail.
Here,the sets are:
$A = \{HTT, THT, TTH\}$
$B = \{HHT, HTH, THH\}$
These events are mutually exclusive because $A \cap B = \phi$.
They are not exhaustive because $A \cup B = \{HTT, THT, TTH, HHT, HTH, THH\} \neq S$.
Explore More
Similar Questions
Two numbers $x$ and $y$ are chosen at random from the set of integers $\{1, 2, 3, 4, \dots, 15\}$. The probability that the point $(x, y)$ lies on a line passing through $(0, 0)$ with a slope of $\frac{2}{3}$ is:
Six faces of an unbiased die are numbered with $2, 3, 5, 7, 11$ and $13$. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is
$A$ bag contains $9$ discs of which $4$ are red,$3$ are blue and $2$ are yellow. The discs are similar in shape and size. $A$ disc is drawn at random from the bag. Calculate the probability that it will be yellow. (in $/9$)
Easy
View Solution$A$,$B$,$C$ are three horses participating in a race. The probability of horse $A$ to win the race is twice that of horse $B$ and the probability of horse $B$ to win is twice that of horse $C$. Then the probabilities of horses $A$,$B$,and $C$ to win the race are respectively:
If $P(A)=0.59, P(B)=0.30$ and $P(A \cap B)=0.21$,then $P(A^{\prime} \cap B^{\prime})$ is equal to
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo