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
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
View Answer
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
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
View Answer
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
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
View Answer
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
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
View Answer
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
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
View Answer
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
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
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
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
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)}.
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