Answer:
Yes she made an error. Explanation is below.
Step-by-step explanation:
Let the sample space for a six sided number cube be S
[tex]n(S) = \{1,2,3,4,5,6\}\\n(S) = 6[/tex]
Let the event of a number getting greater than two be B
[tex]n(B) = \{3,4,5,6\}\\n(B) = 4[/tex]
To find:
the probability of complement of B that is
p(~B) = ?
Solution"
First we need to solve probability for number getting greater than two
[tex]p(B) = \frac{n(B)}{n(S)}[/tex]
Now substituting the values we get
[tex]p(B) = \frac{4}{6}[/tex]
[tex]p(B) = \frac{2}{3}[/tex]
but we need complement of B so
[tex]p(\textrm{complement of B)} = 1 - p(B)\\p(\~B) = 1 - p(B)\\p(\~B) = 1 - \frac{2}{3}\\ =\frac{1}{3} \\[/tex]
P(complement of rolling a number greater than two) = [tex]\frac{1}{3}[/tex]
