Answer:
(c) and (e)
Step-by-step explanation:
Given
[tex]Pr = \frac{2}{3}[/tex]
Required
Which 2 options can be used to simulate the given probability.
The two options are (c) and (e)
The proof is as follows;
Option (c)
We have:
[tex]Rolls = 7[/tex]
A cube has 6 faces. So:
[tex]S = \{1,2,3,4,5,6\}[/tex]
[tex]n(S)=6[/tex]
The probability of getting ones, twos, threes, and fours is:
[tex]Pr = \frac{n(1,2,3,4)}{n(S)}[/tex]
In: [tex]S = \{1,2,3,4,5,6\}[/tex]
[tex]n(1,2,3,4) = 4[/tex]
So:
[tex]Pr = \frac{4}{6}[/tex]
Simplify
[tex]Pr = \frac{2}{3}[/tex]
Option (e)
We have:
[tex]White = 10[/tex]
[tex]Red = 5[/tex]
[tex]Count = 7[/tex]
Record the probability of white.
This is calculated as:
[tex]Pr = \frac{White}{Total}[/tex]
[tex]Pr = \frac{White}{White + Red}[/tex]
[tex]Pr = \frac{10}{10+5}[/tex]
[tex]Pr = \frac{10}{15}[/tex]
Simplify
[tex]Pr = \frac{2}{3}[/tex]
