Question

a marble is selected from a bag containing eight marbles numbered 1 to 8. the number on the marble selected will be recorded as the outcome. consider the following events. event a: the marble selected has an odd number. event b: the marble selected has a number from 3 to 6. give the outcomes for each of the following events. if there is more than one element in the set, separate them with commas. (a) event \a or b\: (b) event \a and b\: (c) the complement of the event b:

Explanation:

Step1: List elements of event A

Event A contains odd - numbered marbles from 1 to 8, so $A=\{1,3,5,7\}$.

Step2: List elements of event B

Event B contains marbles numbered from 3 to 6, so $B = \{3,4,5,6\}$.

Step3: Find $A\cup B$ (A or B)

The union of two sets contains all elements that are in A or B or both. So $A\cup B=\{1,3,4,5,6,7\}$.

Step4: Find $A\cap B$ (A and B)

The intersection of two sets contains all elements that are in both A and B. So $A\cap B = \{3,5\}$.

Step5: Find the complement of B

The sample space $S=\{1,2,3,4,5,6,7,8\}$. The complement of B, $\overline{B}$, contains all elements in the sample - space that are not in B. So $\overline{B}=\{1,2,7,8\}$.

Answer:

(a) $1,3,4,5,6,7$
(b) $3,5$
(c) $1,2,7,8$