Respuesta :
Answer:
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
[tex]= n^C_r\\=^6C_3\\\\=\dfrac{6!}{3!(6-3)!}\\\\=\dfrac{6!}{3!3!}\\\\=20[/tex]
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.
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
Probability of selecting one particular sample =
[tex]\text{P(Sample)} = \dfrac{1}{20} = 0.05[/tex]
Thus, 0.05 is the equally likely probability of selecting one sample.
