Answer:
10.08% probability that over the next 10 days she will choose white chalk 5 times, yellow chalk 4 times, and purple chalk 1 time
Step-by-step explanation:
Arrangments with repetition:
We have n elements.
m are repeating, and they repeat [tex]r_{0}, r_{1}, ..., r_{m}[/tex] times
The number of ways we can arrange them is:
[tex]A = \frac{n!}{r_{0}!r_{1}!...r_{m}!}[/tex]
In this question:
White chalk has a 0.5 probability of being chosen.
Yellow chalk has a 0.4 probability of being chosen.
Purple chalk has a 0.1 probability of being chosen.
What is the probability that over the next 10 days she will choose white chalk 5 times, yellow chalk 4 times, and purple chalk 1 time
Considering the arrangments:
[tex]P = \frac{10!}{5!4!1!}*(0.5)^{5}*(0.4)^{4}*(0.1)^{1} = 0.1008[/tex]
10.08% probability that over the next 10 days she will choose white chalk 5 times, yellow chalk 4 times, and purple chalk 1 time
