(B) When a die is rolled,the sample space $S$ is given by:$S = \{1, 2, 3, 4, 5, 6\}$The event $E$ (die shows $4$) is:$E = \{4\}$The event $F$ (die sho

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) When a die is rolled,the sample space $S$ is given by:$S = \{1, 2, 3, 4, 5, 6\}$The event $E$ (die shows $4$) is:$E = \{4\}$The event $F$ (die shows an even number) is:$F = \{2, 4, 6\}$To check if $E$ and $F$ are mutually exclusive,we find their intersection:$E \cap F = \{4\}$Since $E \cap F \neq \phi$ (where $\phi$ is the empty set),the events $E$ and $F$ are not mutually exclusive.

Class 11 Mathematics Probability Set Based probability

Easy

$A$ die is rolled. Let $E$ be the event "die shows $4$" and $F$ be the event "die shows an even number". Are $E$ and $F$ mutually exclusive?

A
Yes
B
No
C
Cannot be determined
D
None of these

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Probability

Subtopic

Set Based probability

The probability of getting a sum of $9$ when two dice are thrown is

EasyAP EAMCET 2022

View Solution

In a box there are $8$ red,$7$ blue,and $6$ green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

EasyAP EAMCET 2022

View Solution

In the following experiment,specify the appropriate sample space: $A$ person is noting down the number of accidents along a busy highway during a year.

Easy

View Solution

In a lottery containing $35$ tickets,exactly $10$ tickets bear a prize. If a ticket is drawn at random,then the probability of not getting a prize is

EasyAP EAMCET 2022

View Solution

The probability that at least one of the events $A$ and $B$ occurs is $3/5$. If $A$ and $B$ occur simultaneously with probability $1/5$,then $P(A') + P(B')$ is (in $/5$)

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ die is rolled. Let $E$ be the event "die shows $4$" and $F$ be the event "die shows an even number". Are $E$ and $F$ mutually exclusive?

Similar Questions

The probability of getting a sum of $9$ when two dice are thrown is

In a box there are $8$ red,$7$ blue,and $6$ green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

In the following experiment,specify the appropriate sample space: $A$ person is noting down the number of accidents along a busy highway during a year.

In a lottery containing $35$ tickets,exactly $10$ tickets bear a prize. If a ticket is drawn at random,then the probability of not getting a prize is

The probability that at least one of the events $A$ and $B$ occurs is $3/5$. If $A$ and $B$ occur simultaneously with probability $1/5$,then $P(A') + P(B')$ is (in $/5$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module