Three coins are tossed. Describe two events which are mutually exclusive.
(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 $A$ and $B$ are mutually exclusive if they have no common outcomes,i.e.,$A \cap B = \emptyset$.
Let $A$ be the event of getting no heads: $A = \{TTT\}$.
Let $B$ be the event of getting no tails: $B = \{HHH\}$.
Since $A \cap B = \emptyset$,these two events are mutually exclusive.
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Two events $A$ and $B$ are mutually exclusive if they have no common outcomes,i.e.,$A \cap B = \emptyset$.
Let $A$ be the event of getting no heads: $A = \{TTT\}$.
Let $B$ be the event of getting no tails: $B = \{HHH\}$.
Since $A \cap B = \emptyset$,these two events are mutually exclusive.
Explore More
Similar Questions
Boxes $B_1, B_2$,and $B_3$ contain balls as given below:
Box White Black $B_1$ $1$ $2$ $B_2$ $3$ $1$ $B_3$ $2$ $3$
One ball is drawn at random from each box. Then,among the balls drawn,the probability that two are black and one is white,is
| Box | White | Black |
| $B_1$ | $1$ | $2$ |
| $B_2$ | $3$ | $1$ |
| $B_3$ | $2$ | $3$ |
One ball is drawn at random from each box. Then,among the balls drawn,the probability that two are black and one is white,is
$4$-digit numbers are formed using the digits $4, 5, 6, 7, 8, 9$ allowing repetition of the given digits. If a number is chosen at random from those numbers thus formed,then the probability that it is exactly divisible by $3$ is
Let $S$ be a set containing $n$ elements. If we select $2$ subsets $A$ and $B$ of $S$ at random,then the probability that $A \cup B = S$ and $A \cap B = \phi$ is:
Difficult
View Solution$A$ box contains $6$ red marbles numbered from $1$ through $6$ and $4$ white marbles numbered $12$ through $15$. Find the probability that a marble drawn at random is white and odd-numbered.
$A$ man and a woman appear in an interview for two vacancies in the same post. The probability of the man's selection is $1/4$ and that of the woman's selection is $1/3$. What is the probability that none of them will be selected?
Medium
View SolutionVedclass 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