Short Answer Type
Long Answer TypeAn experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
A : The sum is greater than 8.
B : 2 occurs on either die.
C : The sum is at least 7 and a multiple of 3.
Which pairs of these events are mutually exclusive?
A pair of dice is rolled.
∴ The sample space is:
S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
Event A: the sum of numbers on the two dice is greater than 8.
A = {(3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6)}
Event B: two occurs on either die
Two occurs on first die, the second die or both.
B = {(1,2), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,2), (4,2), (5,2), (6,2)}
Event C: the sum is at least 7 and is divisible by 3
C = {(3,6), (4,5), (5,4), (6,3), (6,6)}
Now, 
= {(3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6)}
{(1,2), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,2), (4,2), (5,2), (6,2)}
=
∴ A and B are mutually exclusive.
= {(3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6)}
{(3,6), (4,5), (5,4), (6,3), (6,6)}
= {(3,6), (4,5), (5,4), (6,3), (6,6) 
∴ A and C are not mutually exclusive.
= {(1,2), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,2), (4,2), (5,2), (6,2)}
{(3,6), (4,5), (5,4), (6,3), (6,6)}
= 
∴ B and C are mutually exclusive.
Two dice are thrown. The events A, B, C are as follows:
A = Getting an odd number on the first die.
B = Getting a total of 7 on the two dice.
C = Getting a sum ≥ 8 on the two dice.
Describe events:
(i) A' (ii) not B (iii) A or B (iv) B and C (v) A but not C (vi) B but not C (vii) B or C
Short Answer TypeTwo 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 whether the following is true or false (give reason for your answer):
A and B are mutually exclusive.
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 whether the following is true or false (give reason for your answer):
A and B arc mutually exclusive and exhaustive.
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 whether the following is true or false (give reason for your answer):
A = B'
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 whether the following is true or false (give reason for your answer):
A and C are mutually exclusive.
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