Mathematics: (a) Count the number of ways to select a sample of 3 people to serve on a board of directors from a population of 6 people. (b) If a simple random sampling procedure is to be employed, the chances that any particular sample will be the one selected are

Y=7 and x=−2 are the answers...

(a) Count the number of ways to select a sample

odalyarreola18

20.01.2022

a) 20

b) Equally likely, 0.05

Step-by-step explanation:

We are given the following in the question:

Population size, n = 6

Sample size, r = 3

a) Ways to select a sample of 3 from a population of 6

$= n^C_r\\=^6C_3\\\\=\dfrac{6!}{3!(6-3)!}\\\\=\dfrac{6!}{3!3!}\\\\=20$

Thus, there are 20 ways in which a sample of 3 can be selected from a population of 6.

b) The chances that any particular sample will be the one selected are equally likely.

$\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

Probability of selecting one particular sample =

$\text{P(Sample)} = \dfrac{1}{20} = 0.05$

Thus, 0.05 is the equally likely probability of selecting one sample.

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