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 \( \overline{F}\)

Asked by Aaryan | 1 year ago | 41

Given: A dice is thrown once.

Let us find the given events, and also find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and \( \overline{F}\)

S = {1, 2, 3, 4, 5, 6}

According to the subparts of the question, we have certain events as:

**(i)** A = getting a number below 7

So, the sample spaces for A are:

A = {1, 2, 3, 4, 5, 6}

**(ii)** B = Getting a number greater than 7

So, the sample spaces for B are:

B = {Փ}

**(iii)** C = Getting multiple of 3

So, the Sample space of C is

C = {3, 6}

**(iv)** D = Getting a number less than 4

So, the sample space for D is

D = {1, 2, 3}

**(v)** E = Getting an even number greater than 4.

So, the sample space for E is

E = {6}

**(vi)** F = Getting a number not less than 3.

So, the sample space for F is

F = {3, 4, 5, 6}

Now,

A = {1, 2, 3, 4, 5, 6} and B = {Փ}

A ⋃ B = {1, 2, 3, 4, 5, 6}

A = {1, 2, 3, 4, 5, 6} and B = {Փ}

A ⋂ B = {Փ}

B = {Փ} and C = {3, 6}

B ⋂ C = {Փ}

F = {3, 4, 5, 6} and E = {6}

E ⋂ F = {6}

E = {6} and D = {1, 2, 3}

D ⋂ F = {3}

Answered by Aaryan | 1 year agoOne number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?

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