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 4

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

Answer 1

Since a die was thrown. So elementary events are
{1}, {2}, {3}, {4}, {5}, {6}

(i) A = {1,2,3,4,5,6}

(ii) B = Getting a number greater than 7.
$B=\varphi$

[$\because$ A die has 1, 2, 3, 4, 5, 6 members only}

(iii) = Getting a multiple of 3.
C = (3, 6}

(iv) D = Getting a number less than 4.
D = {1, 2, 3}

(v) E = Getting an even number greater than 4.
E= {6}

(vi) F = Getting a number not less than 3.
F= {3,4,5,6}

Also, $A\cup B=\{1,2,3,4,5,6\}A\cap B=\left\{\varphi \right\}B\cap C=\left\{\varphi \right\}E\cap F=\left\{6\right\}D\cap F=\left\{3\right\}$

$\overrightarrow{F}=1-F=\{1,2\}$