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)=(4)/(6)\Rightarrow P(A)=(2)/(3) \\ \\ and \\ \\ P(B)=(3)/(6)\Rightarrow P(B)=(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`