# Mathematics Questions and Answers – Probability – Events-2

«

This set of Mathematics Aptitude Test for IIT JEE Exam focuses on “Probability – Events-2”.

1. Event _____________ contains elements which are either in A or in B or in both.
a) A or B
b) A and B
c) A but not B
d) B but not A

Explanation: Event “A or B” contains elements which are either in A or in B or in both. It is also called union of the two sets.

2. Event “A or B” is represented by _____________
a) A∪B
b) A∩B
c) A∩B’
d) A’∩B

Explanation: Event “A or B” contains elements which are either in A or in B or in both. It is also called union of the two sets and is represented by A∪B.

3. Event “A and B” is represented by _____________
a) A∪B
b) A∩B
c) A∩B’
d) A’∩B

Explanation: Event “A and B” contains elements which are both in A and B. It is also called intersection of two sets and is represented by A∩B.

4. Event _____________ contains elements which are present in both A as well as B.
a) A or B
b) A and B
c) A but not B
d) B but not A

Explanation: Event “A and B” contains elements which are in A as well as B. It is also called intersection of the two sets.

5. Event _____________ contains elements which are present in A and absent in B.
a) A or B
b) A and B
c) A but not B
d) B but not A

Explanation: Event “A but not B” contains elements which are present in A but not in B.
It is represented by A-B or A∩B’.

6. Event _____________ contains elements which are present in B and absent in A.
a) A or B
b) A and B
c) A but not B
d) B but not A

Explanation: Event “B but not A” contains elements which are present in B but not in A.
It is represented by B-A or B∩A’.

7. Event “A but not B” is represented by _____________
a) A∪B
b) A∩B
c) A∩B’
d) A’∩B

Explanation: Event “A but not B” contains elements which are present in A but not in B.
It is represented by A-B or A∩B’.

8. Event “B but not A” is represented by _____________
a) A∪B
b) A∩B
c) A∩B’
d) A’∩B

Explanation: Event “B but not A” contains elements which are present in B but not in A.
It is represented by B-A or B∩A’.

9. If A∩B=ϕ then set is said to be mutually exhaustive.
a) True
b) False

Explanation: If A∩B=ϕ then set is said to be mutually exclusive not mutually exhaustive. If both sets A and B have no element in common then it is a pair of mutually exclusive sets.

10. If A∪B=S then set is said to be mutually exhaustive.
a) True
b) False

Explanation: If A∪B=S then set is said to be mutually exhaustive. If both sets A and B have together form sample space then it is a pair of mutually exhaustive sets.

11. Two dice are thrown simultaneously. Let A be the event of getting sum less than 4 and B be the event of getting sum not more than 4. Find set “A or B”.
a) {(1,1), (1,2), (2,1)}
b) {}
c) {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}
d) {(1,3), (2,2), (3,1)}

Explanation: A = {(1,1), (1,2), (2,1)}
B= {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}
“A or B” contains elements of either A or B or both.
So, A or B = {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}.

12. Two dice are thrown simultaneously. Let A be the event of getting sum less than 4 and B be the event of getting sum not more than 4. Find set “A and B”.
a) {(1,1), (1,2), (2,1)}
b) {}
c) {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}
d) {(1,3), (2,2), (3,1)}

Explanation: A = {(1,1), (1,2), (2,1)}
B= {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}
“A and B” contains elements present in both A and B.
So, A and B = {(1,1), (1,2), (2,1)}.

13. Two dice are thrown simultaneously. Let A be the event of getting sum less than 4 and B be the event of getting sum not more than 4. Find set “A and not B”.
a) {(1,1), (1,2), (2,1)}
b) {}
c) {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}
d) {(1,3), (2,2), (3,1)}

Explanation: A = {(1,1), (1,2), (2,1)}
B= {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}
“A and not B” contains elements which are in A but not in B.
So, A and not B = {}.

14. Two dice are thrown simultaneously. Let A be the event of getting sum less than 4 and B be the event of getting sum not more than 4. Find set “B and not A”.
a) {(1,1), (1,2), (2,1)}
b) {}
c) {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}
d) {(1,3), (2,2), (3,1)}

Explanation: A = {(1,1), (1,2), (2,1)}
B= {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}
“B and not A” contains elements which are in B but not in A.
So, B and not A = {(1,3), (2,2), (3,1)}.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

To practice Mathematics Aptitude Test for IIT JEE Exam, here is complete set of 1000+ Multiple Choice Questions and Answers.

Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs! 