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Straight Lines

Question
CBSEENMA11014635
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An 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? 

Solution

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.
rightwards double arrow             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
rightwards double arrow Two occurs on first die, the second die or both.
rightwards double arrow                  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
rightwards double arrow             C = {(3,6), (4,5), (5,4), (6,3), (6,6)}
Now,   straight A intersection straight B = {(3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6)}
                  space intersection {(1,2), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,2), (4,2), (5,2), (6,2)}
                   =straight ϕ
∴ A and B are mutually exclusive.
         straight A intersection straight C = {(3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6)}
                                                          space intersection {(3,6), (4,5), (5,4), (6,3), (6,6)}
                  = {(3,6), (4,5), (5,4), (6,3), (6,6) space space not equal to straight ϕ
∴ A and C are not mutually exclusive.
         space straight B intersection straight C = {(1,2), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,2), (4,2), (5,2), (6,2)}
                                                                  space intersection {(3,6), (4,5), (5,4), (6,3), (6,6)}
                   = straight ϕ
∴ B and C are mutually exclusive.

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Some More Questions From Straight Lines Chapter

Describe the sample space S, when a die is tossed once .

An experiment consists of recording boy-girl composition of families with 2 children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

 

An experiment consists of recording boy-girl composition of families with 2 children. What is the sample space if we are interested in the number of girls in the family?

 

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

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