91Ó°ÊÓ

A jury is formed by selecting 12 possible jurors at random from a pool of 10 men and 8 women.

All possible outcomes are represented in the sample space. A jury of 12 people is required, thus at least 4 men will be chosen out of the total of 8 women.

$S=\{4,5,6,7,8,9,10\}$

A is a event in which at least half of the jury members are male.

$A=\{6,7,8,9,10\}$

B is an event in which at least half of the eight women on the jury are female. As a result, the jury will consist of a maximum of 8 men and a minimum of 6.

$B=\{6,7,8\}$

Now

role="math" localid="1651472188677" $$\begin{gathered} (AorB)=\{6,7,8,9,10\} \\ (A\&B )=(6,7,8) \\ (A(notB\left)\right)=\{9,10\} \end{gathered}$$

A jury is formed by selecting 12 possible jurors at random from a pool of 10 men and 8 women.

$$\begin{gathered} Aâˆ\copyright B≠\mathrm{Ï•} \\ Aâˆ\copyright B^{\text{'}}≠\mathrm{Ï•} \\ {A}^{\text{'}}âˆ\copyright B^{\text{'}}≠\mathrm{Ï•} \end{gathered}$$

$AandB$are not mutually exclusive.

$Aand(notB)$are not mutually exclusive and

$(notA)and(notB)$are not mutually exclusive.