Mastery Check Solutions

1. An odd number or a multiple of 5 is rolled.

$$\begin{gathered} \mathrm{Odd}: \left\{1, 3, 3, 5, 5, 9, 15, 15, 25\right\} \\ \mathrm{Multiple} \mathrm{of} 5:\left\{5, 5, 10, 10, 15, 15, 20, 20, 25, 30, 30\right\} \\ \mathrm{P}\left(\mathrm{odd} \cup \mathrm{multiple} \mathrm{of} 5\right)=\frac{9}{36}+\frac{11}{36}–\frac{5}{36}=\frac{15}{36}=\frac{5}{12} \end{gathered}$$

2. $\mathrm{P}(\mathrm{perfect} \mathrm{square} \cup \mathrm{product} \mathrm{is} 6)$

$$\begin{gathered} \mathrm{Perfect} \mathrm{square}: \left\{1, 4, 4, 4, 9, 16, 25, 36\right\} \\ \mathrm{Product} \mathrm{is} 6:\hspace{0.17em}\left\{6, 6, 6, 6\right\} \\ \mathrm{P}(\mathrm{perfect} \mathrm{square} \cup \mathrm{product} \mathrm{is} 6)=\frac{8}{36}+\frac{4}{36}=\frac{12}{36}=\frac{1}{3} \end{gathered}$$

3. $\mathrm{P}(\mathrm{prime} \cap \mathrm{factor} \mathrm{of} 36)$

$$\begin{gathered} \mathrm{Prime}: \left\{\mathbf{2}\mathbf{,}\mathbf{ }\mathbf{2}, \mathbf{3}\mathbf{,}\mathbf{ }\mathbf{3}, 5, 5\right\} \\ \mathrm{Factor} \mathrm{of} 36: \left\{1, \mathbf{2}\mathbf{,}\mathbf{ }\mathbf{2}, \mathbf{3}\mathbf{,}\mathbf{ }\mathbf{3}, 4, 4, 4, 6, 6, 6, 6, 9, 12, 12, 12, 12, 18, 18, 36\right\} \\ \mathrm{P}(\mathrm{prime} \cap \mathrm{factor} \mathrm{of} 36)=\frac{4}{36}=\frac{1}{9} \end{gathered}$$

4. Explain if a Venn diagram with the subsets labeled “Sum is even” and “Sum is odd” represents mutually exclusive or inclusive events.

The diagram would represent mutually exclusive events because the sum cannot be even and odd at the same time.

5. Construct a two-way table that groups the numbers by multiples of two and multiples of three.

Multiple of two: {2, 4, 6, 8, 10, 12}
Multiple of three: {3, 6, 9, 12}
Multiple of two and three: {6, 12}
Neither: {5, 7, 11}