4b) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible simple events can be represented as follows: ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on board. The events A and B are defined as follows: A= event that Betty and Allison are both selected B = event that Charlie and Dave are both selected Then the events A and B mutually exclusive. True False the

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**Problem 4b: Selecting Board Members for a Nonprofit Organization**

*Scenario:*
Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. 

*Possible Simple Events:*
The possible combinations (simple events) of selecting 3 out of the 5 members can be represented as:

- ABC
- ABD
- ABE
- ACD
- ACE
- ADE
- BCD
- BCE
- BDE
- CDE

*Example:*
For example, "ABC" represents the outcome that Allison, Betty, and Charlie are selected to be on the board.

*Defined Events:*
The events A and B are defined as follows:
- **A** = event that Betty and Allison are both selected.
- **B** = event that Charlie and Dave are both selected.

*Question:*
Are the events A and B mutually exclusive?

**Options:**
- True ☐
- False ☐
Transcribed Image Text:**Problem 4b: Selecting Board Members for a Nonprofit Organization** *Scenario:* Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. *Possible Simple Events:* The possible combinations (simple events) of selecting 3 out of the 5 members can be represented as: - ABC - ABD - ABE - ACD - ACE - ADE - BCD - BCE - BDE - CDE *Example:* For example, "ABC" represents the outcome that Allison, Betty, and Charlie are selected to be on the board. *Defined Events:* The events A and B are defined as follows: - **A** = event that Betty and Allison are both selected. - **B** = event that Charlie and Dave are both selected. *Question:* Are the events A and B mutually exclusive? **Options:** - True ☐ - False ☐
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