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fomenos
3 years ago
7

Consider a political discussion group consisting of 8 ​Democrats, 5 ​Republicans, and 5 Independents. Suppose that two group mem

bers are randomly​ selected, in​ succession, to attend a political convention. Find the probability of selecting two Independents.
Mathematics
1 answer:
Leya [2.2K]3 years ago
7 0

Answer:

The probability of selecting two Independents is \frac{10}{153}.

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

8+5+5=18

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

^{n}C_r=\frac{n!}{r!(n-r)!}

Total number of ways to select 2 members from 18 members is

\text{Total possible outcomes}=^{18}C_2=\frac{18!}{2!(18-2)!}=153

Total number of ways to select 2 members from 5 Independents is

\text{Favorable outcomes}=^{5}C_2=\frac{5!}{2!(5-2)!}=10

The probability of selecting two Independents is

p=\frac{\text{Favorable outcomes}}{\text{Total possible outcomes}}

p=\frac{10}{153}

Therefore the probability of selecting two Independents is \frac{10}{153}.

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