Mathematics Questions and Answers – Probability – Events-2

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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
View Answer

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

Answer: 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 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
View Answer

Answer: 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.
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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
View Answer

Answer: b
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
View Answer

Answer: c
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’.
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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
View Answer

Answer: d
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
View Answer

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

Answer: d
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
View Answer

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

Answer: b
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)}
View Answer

Answer: c
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)}
View Answer

Answer: a
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)}
View Answer

Answer: b
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)}
View Answer

Answer: d
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.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter