Short Answer TypeThree coins are tossed.
Sample space is: S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Event A = at least two heads show
A = {HHH, HHT, HTH, THH}
Event B = exactly one head shows
B = {HTT, THT, TTH}
Event C = no head appears
C = {TTT}
Now, 
A and B are mutually exclusive
B and C are mutually exclusive
A and C are mutually exclusive
∴ A, B, C are mutually exclusive events.
Also, 
= {HHH, HHT, HTH, THH}
{HTT, THT, TTH}
{TTT}
= {HHH, HHT, HTH, THH, HTT, THT, TTH}
{TTT}
= {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} = S
∴ A, B, C are exhaustive events.
Hence, A, B and C are mutually exclusive and exhaustive events.
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?
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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