Respuesta :
Answer:
Option D - [tex]\frac{2}{7}[/tex].
Step-by-step explanation:
Given : From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event.
To find : What is the probability that Andrew will be among the 4 volunteers selected and Karen will not?
Solution :
Choosing 4 people out of 8 volunteers is [tex]^8C_4[/tex]
[tex]^8C_4=\frac{8!}{4!(8-4)!}[/tex]
[tex]^8C_4=\frac{8\times 7\times 6\times 5\times 4!}{4!\times 4\times 3\times 2}[/tex]
[tex]^8C_4=70[/tex]
Choosing a group of 4 with Andrew and no karein is given by,
One position is fixed by Andrew and Karein the number of volunteer left is 6.
Rest 3 volunteers is chosen from 6.
Choosing 3 people out of 6 volunteers is [tex]^6C_3[/tex]
[tex]^6C_3=\frac{6!}{3!(6-3)!}[/tex]
[tex]^6C_3=\frac{6\times 5\times 4\times 3!}{3!\times 3\times 2}[/tex]
[tex]^6C_3=20[/tex]
The probability that Andrew will be among the 4 volunteers selected and Karen will not is given by,
[tex]P=\frac{^6C_3}{^8C_4}[/tex]
[tex]P=\frac{20}{70}[/tex]
[tex]P=\frac{2}{7}[/tex]
The probability that Andrew will be among the 4 volunteers selected and Karen will not is [tex]\frac{2}{7}[/tex].
Therefore, option D is correct.
