Question 1039539: 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, Bob, Charlie, Dave, and Emily. The possible outcomes can be represented as follows.
ABC ABD ABE ACD ACE
ADE BCD BCE BDE CDE
Here, for example, ABC represents the outcome that Allison, Bob, and Charlie are selected to be on the board. The events A and B are defined as follows.
A = event that Dave is selected
B = event that fewer than two men are selected
List the outcomes that comprise the event (A & B).?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
In this day and age of blurred gender identities, one has to make some assumptions regarding the data provided in the stem of this question. My response assumes that Allison and Emily are not men and that Bob, Charlie, and Dave are men.
Fewer than two men selected means that either 0 men are selected or 1 man is selected. Since event A requires that Dave is selected, that eliminates the possibility of 0 men being selected, and eliminates any element of the sample space that contains either Bob or Charlie. Further, since all elements of the sample space each have three elements, and there is exactly one man, the other two elements must be "not men". There are only 2 "not men" available, namely Allison and Emily.
Therefore, there is exactly one element of the sample space that represents a successful outcome of event (A & B), namely ADE.
John
My calculator said it, I believe it, that settles it
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