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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