Respuesta :
The combined probability of picking three yellow marbles [tex]= (\frac{14}{285} )[/tex]
It is NOT a binomial experiment.
Step-by-step explanation:
Here, the total number of marbles in the bag = 20
The total number of green marbles = 12
The total number of yellow marbles = 8
Now, let E : Event of picking a picking a yellow marble
[tex]P(E) = \frac{\textrm{THe total number of yellow marbles}}{\textrm{The total marbles in the bag}}[/tex]
So, the probability of picking FIRST yellow marble = [tex]\frac{8}{20} = (\frac{2}{5})[/tex]
Now,as the marbles is again picked WITHOUT REPLACEMENT:
So, total marbles in the bag now = 20 -1 = 19 and yellow marbles = 8 -1 = 7
P(Picking second yellow marble) = [tex](\frac{7}{19} )[/tex]
P(Picking Third yellow marble) = [tex](\frac{6}{18} ) = (\frac{1}{3} )[/tex]
Now the combined probability of picking three yellow marbles
= [tex](\frac{2}{5} ) \times (\frac{7}{19} ) \times (\frac{1}{3} ) = (\frac{14}{285} )[/tex]
Also, the binomial experiment = [tex]^n C_x(p)^x(q)^{n-x[/tex]
Solving for n = 20 and x = 3 , p = 2/5 and q = 3/5 we get:
P = [tex]^{20}C_3 (\frac{2}{5})^3(\frac{3}{5} )^{17} = 1140 \times \frac{8}{125} \times\frac{3^{17}}{5^{17}}[/tex] ≠[tex](\frac{14}{285})[/tex]
Hence, it is NOT a binomial experiment.
