Consider a political discussion group consisting of 8 ​Democrats, 5 ​Republicans, and 5 Independents. Suppose that two group members are randomly​ selected, in​ succession, to attend a political convention. Find the probability of selecting two Independents.

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 = 8Republicans = 5Independents = 5Total 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].