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Question

In a single throw of a die describe the following events:
(i) A = Getting a number less than 7
(ii) B = Getting a number greater than 7
(iii) C = Getting a multiple of 3
(iv) D = Getting a number less than 4
(v) E = Getting an even number greater than 4
(vi) F = Getting a number not less than 3.
Also, find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and F.

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Solution

When a dice is thrown, the sample space is given by S = {1, 2, 3, 4, 5, 6}.
Accordingly, we have:
(i) A = {1, 2, 3, 4, 5, 6}
(ii) B = Φ
(iii) C = {3, 6}
(iv) D = {1, 2, 3}
(v) E = {6}
(vi) F = {3, 4, 5, 6}

Here, A = {1, 2, 3, 4, 5, 6} and B = Φ
∴ A ∪ B = {1, 2, 3, 4, 5, 6}

Here, A = {1, 2, 3, 4, 5, 6} and B = Φ
∴ A ∩ B = Φ

Here, B = Φ and C = {3, 6}
∴ B ∩ C = Φ

Here, E = {6} and F = {3, 4, 5, 6}
∴ E ∩ F = {6}

Here, D = {1, 2, 3} and F = {3, 4, 5, 6}
∴ D ∩ F = {3}


Here, F = {3, 4, 5, 6} and S = {1, 2, 3, 4, 5, 6}
F¯=S-F={1,2}

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