Question

• COUNTING AND PROBABILITYDetermining outcomes for compound events and complements...A number cube with faces labeled 1 to 6 is rolled once.The number rolled will be recorded as the outcome.Consider the following events.Event A: The number rolled is less than 5. IsEvent B The number rolled is even:Give the outcomes for each of the following events.If there is more than one element in the set, separate them with commas.(a) Event "A and B": (1)0O.(b) Event "A or B*: (L)(c) The complement of the event B:

Answer 1

We will have the following:

First, e have that the probability for A and B are respectively:

$\begin{gathered} P(A)=\frac{4}{6}\Rightarrow P(A)=\frac{2}{3} \\ \\ and \\ \\ P(B)=\frac{3}{6}\Rightarrow P(B)=\frac{1}{3} \end{gathered}$

Now:

a) Event "A and B":

${}{}\lbrace2,4\rbrace$

b) Event "A or B":

$\lbrace1,3,5,6\rbrace$

c) The complement of the event B is:

$\lbrace1,3,5\rbrace$