Respuesta :
Answer:
The probability of selecting two Independents is [tex]\frac{10}{153}[/tex].
Step-by-step explanation:
From the given information it is clear that:
Democrats = 8
Republicans = 5
Independents = 5
Total number of member in the group is
[tex]8+5+5=18[/tex]
We need to find the probability of selecting two Independents.
According to binomial distribution the total number of ways to select r items form n items is
[tex]^{n}C_r=\frac{n!}{r!(n-r)!}[/tex]
Total number of ways to select 2 members from 18 members is
[tex]\text{Total possible outcomes}=^{18}C_2=\frac{18!}{2!(18-2)!}=153[/tex]
Total number of ways to select 2 members from 5 Independents is
[tex]\text{Favorable outcomes}=^{5}C_2=\frac{5!}{2!(5-2)!}=10[/tex]
The probability of selecting two Independents is
[tex]p=\frac{\text{Favorable outcomes}}{\text{Total possible outcomes}}[/tex]
[tex]p=\frac{10}{153}[/tex]
Therefore the probability of selecting two Independents is [tex]\frac{10}{153}[/tex].
