Answer:
0.032% probability of this happening
Step-by-step explanation:
Since the distribution is very large(10,000 skittles), and there are only two possible outcomes(either the Skittles is green or it is not) we can use the binomial probability distribution as an approximation.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Handful of 5 skittles:
This means that [tex]n = 5[/tex]
20% of the Skittles are green
This means that [tex]p = 0.2[/tex]
What is the probability of this happening?
Probability of all skittles being green, so [tex]P(X = 5)[/tex].
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.2)^{5}.(0.8)^{0} = 0.00032[/tex]
0.032% probability of this happening
