Answer:
The probability that Andrew will be among the 4 volunteers selected and Karen will not is 2/7.
Step-by-step explanation:
From the given information it is clear that
The total number of volunteers, including Andrew and Karen = 8
The total number of volunteers, excluding Andrew and Karen = 8-2 = 6
We need to find the probability that Andrew will be among the 4 volunteers selected and Karen will not.
Total number of ways of selecting r volunteers from n volunteers is
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Total number of ways of selecting 4 volunteers from 8 volunteers is
[tex]\text{Total outcomes}=^8C_4=70[/tex]
Total number of ways of selecting 4 volunteers from 8 volunteers, so that Andrew will be among the 4 volunteers selected and Karen will not is
[tex]\text{Favorable outcomes}=^1C_1\times ^6C_3=1\times 20=20[/tex]
The probability that Andrew will be among the 4 volunteers selected and Karen will not is
[tex]P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]P=\frac{20}{70}[/tex]
[tex]P=\frac{2}{7}[/tex]
Therefore the probability that Andrew will be among the 4 volunteers selected and Karen will not is 2/7.
