Question

A marble is selected from a bag containing eight marbles numbered 1 to 8. The number of the marble selected will be recorded as the outcome. Consider the following events. Event A: The marble selected has an even number.

Event B: The marble selected has a number from 3 to 6.
a) Event "A or B":
b) Event "A and B":
c) The complement of the event A.

Answer 1

• Answer:

A) - Event "A or B" Consists of the Outcomes:

{2, 3, 4, 5, 6, 8}

B) - Event "A or "B" Consists of the Outcomes:

{4, 6}

C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:

{1, 3, 5, 7}

• Explanation:

MAKE A PLAN:

List The OUTCOMES for EACH EVENT and their COMBINATIONS:

• SOLVE THE PROBLEM:

a) - EVENT "A": {2, 4, 6, 8}

EVENT "B": {3, 4, 5, 6}

EVENT "A" or "B": {2, 3, 4, 5, 6, 8}

b) - EVENT "A" or "B": {4, 6}

c) - The COMPLEMENT of the EVENT "A": {1, 3, 5, 7}

• Draw the conclusion:

A) - Event "A or B" Consists of the Outcomes:

{2, 3, 4, 5, 6, 8}

B) - Event "A or "B" Consists of the Outcomes:

{4, 6}

C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:

{1, 3, 5, 7}

I hope this helps!

Answer 2

a) Event "A or B" refers to the marble selected having either an even number or a number from 3 to 6. To determine the outcomes that satisfy this event, we need to identify the numbers that meet either condition.

Even numbers: 2, 4, 6, 8
Numbers from 3 to 6: 3, 4, 5, 6

Combining these sets and removing duplicates, we have the following outcomes: 2, 3, 4, 5, 6, 8. So, event "A or B" includes these outcomes.

b) Event "A and B" refers to the marble selected having both an even number and a number from 3 to 6. To determine the outcomes that satisfy this event, we need to find the numbers that meet both conditions.

Numbers that are both even and from 3 to 6: 4, 6

Therefore, event "A and B" includes the outcome of either 4 or 6.

c) The complement of event A refers to outcomes that are not part of event A. Since event A represents the marble selected having an even number, the complement of event A would be the marble selected having an odd number.

Odd numbers: 1, 3, 5, 7

Therefore, the complement of event A includes these outcomes.