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Exhaustive Events

Refer to ques...

Question

Refer to question 6 above, state true or false (give reason for your answer)
(i) A and B are mutually exclusive
(ii) A and B are mutually exclusive and exhaustive
(iii) A = B'
(iv) A and C are mutually exclusive
(v) A and B' are mutually exclusive
(vi) A' B', C are mutually exclusive and exhaustive.

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Solution

taking A, B, C events from question 6 Above we have
(i) $A \cap B = ϕ$
Thus A and B are mutually exclusive events.
$∴$ True.
(ii) $A \cap B = ϕ a n d A \cap B = S$
Thus A and B are mutually exclusive and exhaustive events.
$∴$ True.
(iii) $B^{'} = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}$
= A
$∴ T r u e$
$(i v) A \cap c = {(2, 1), (2, 2), (2, 3), (4, 1)} = ϕ$
Thus A and c are not mutually exclusive events $∴$ False
(v) $A \cap B^{'} = A \neq ϕ$
Thus A and B' are not mutually exclusive events.
(vi) Since $A^{'} = B a n d B^{'} = A, A \cap B = ϕ$
$B \cap C = {(1, 1), (1, 2), (1, 3), (1, 4), (3, 1), (3, 2)}$
$\neq ϕ$
$A \cap C = {(2, 1), (2, 2), (2, 3), (4, 1)}$
$= ϕ$
Thus A', B' and C are not mutually exclusive.
$∴$ False.

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Similar questions

Two dice are thrown. The events A, B and C are as follows:

A: getting an even number on the first die.

B: getting an odd number on the first die.

C: getting the sum of the numbers on the dice ≤ 5

State true or false: (give reason for your answer)

(i) A and B are mutually exclusive

(ii) A and B are mutually exclusive and exhaustive

(iii)

(iv) A and C are mutually exclusive

(v) A and are mutually exclusive

(vi) are mutually exclusive and exhaustive.

Q. Two dice are thrown. The events

A, B and C

are as follows:

A :

getting an even number on the first die.

B :

getting an odd number on the first die.

C :

getting the sum of the numbers on the dice

\leq 5

i .

State true or false: (give reason for your answer)

A

B

are mutually exclusive.

i i .

State true or false: (give reason for your answer)

A

B

are mutually exclusive and exhaustive.

i i i .

State true or false: (give reason for your answer)

A = B'

i v .

State true or false: (give reason for your answer)

A

C

are mutually exclusive.

v .

State true or false: (give reason for your answer)

A

B^{'}

are mutually exclusive.

v i .

State true or false: (give reason for your answer)

A', B', C

are mutually exclusive and exhaustive.

Q. Three coins are tossed. Describe.
(i) two events A and B which are mutually exclusive.
(ii) three events A, B and C which are mutually exclusive and exhaustive.
(iii) two events A and B which are not mutually exclusive.
(iv) two events A and B which are mutually exclusive but not exhaustive.

Three coins are tossed. Describe
(i) two events A and B which are mutually exclusive.

(ii) three events A, B and C which are mutually exclusive and exhaustive.

(iii) two events A and B which am not mutually exclusive.

(iv) two events A and B which are mutually exclusive but not exhaustive.

Two dice are thrown. The events A, B, C, D, E and F are described as follows :

A = Getting an even number on the first die.

B = Getting an odd number on the first die.

C = Getting at most 5 as sum of the numbers on the two dice.

D = Getting the sum of the numbers on the dice greater than 5 but less than 10.

E = Getting at least 10 as the sum of the numbers on the dice.

F = Getting an odd number on one of the dice.

(i) Describe the following events : A and B, B or C, B and C, A and E, A or F, A and F

(ii) State true or false :

(a) A and B are mutually exclusive.

(b) A and B are mutually exclusive and exhaustive events.

(c) A and C are mutually exclusive events.

(d) C and D are mutually exclusive and exhaustive events.

(e) C, D and E are mutually exclusive and exhaustive events.

(f) A' and B' are mutually exclusive events.

(g) A, B, F arc mutually exclusive and exhaustive events.

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