Practice 1 Solutions

B’

$A \cup B$

3. $A \cap B$

4. A

5. What is the difference between mutually exclusive and inclusive?

Sample: Mutually exclusive events do not have any overlapping events (intersecting events). Inclusive events have at least one event that is in the intersection of the sets.

6. What is a compound event in probability?

A compound event in probability is made up of two or more simple events.

$\begin{array}{rcl}\mathrm{P}\left(\mathrm{Face}\right)+\mathrm{P}\left(\mathrm{A}\right)& =& \frac{3+3+3+3}{52}+\frac{4}{52}=\frac{16}{52}\end{array}$

$\frac{4}{13}$

8. $\mathrm{P}(\mathrm{seven} \cup \mathrm{clubs})$

$$\begin{gathered} \mathrm{P}\left(7 \cup \mathrm{clubs}\right) \\ \mathrm{P}\left(7\right)+\mathrm{P}(♣)–\mathrm{P}(7♣)=\frac{4}{52}+\frac{13}{52}–\frac{1}{52}=\frac{16}{52} \end{gathered}$$

$\frac{4}{13}$

9. $\mathrm{P}(\mathrm{two} \mathrm{or} \mathrm{red})$

$$\begin{gathered} \mathrm{P}\left(2 \cup \mathrm{red}\right) \\ \mathrm{P}\left(2\right)+\mathrm{P}\left(\mathrm{red}\right)–\mathrm{P}(2♥\mathrm{,}️♦)=\frac{4}{52}+\frac{26}{52}–\frac{2}{52}=\frac{28}{52} \end{gathered}$$

$\frac{7}{13}$

10. Probability of a red two

$$\begin{gathered} \mathrm{P}(\mathrm{red} \cap 2) \\ \mathrm{P}(2♥,️2♦)=\frac{2}{52} \end{gathered}$$

$\frac{1}{26}$

11. $\mathrm{P}(\mathrm{five} \mathrm{and} \mathrm{six})$

$\mathrm{P}\left(5 \cap 6\right)=0$

0

12. Which problems are mutually exclusive? Explain.

Sample: Problems 7 and 11 are mutually exclusive because the events in these sets do not intersect.

13. Create a two-way table.

Prime, P: {5, 7, 11, 13}
Even, E: {4, 6, 8, 10, 12, 14}
Not even and not prime: {9, 15}
Prime and even: none

14. Create a Venn diagram.

Prime, P: {5, 7, 11, 13}
Even, E: {4, 6, 8, 10, 12, 14}
Not even and not prime: {9, 15}
Prime and even: none

15. $\mathrm{P}(\mathrm{multiple} \mathrm{of} 3 \mathrm{or} \mathrm{even})$

Multiple of 3: {6, 9, 12, 15}

$\begin{array}{rcl}\mathrm{P}\left(\mathrm{mult} \mathrm{of} 3\right)+\mathrm{P}\left(\mathrm{even}\right)–\mathrm{P}\left(\mathrm{mult} 3 \cap \mathrm{even}\right)& =& \frac{4}{12}+\frac{6}{12}–\frac{2}{12}=\frac{8}{12}\end{array}$

$\frac{2}{3}$

16. $\mathrm{P}(\mathrm{factor} \mathrm{of} 15 \mathrm{and} \mathrm{prime})$

Factors of 15: {5, 15}

$P\left(\mathrm{factor} \mathrm{of} 15 \cap P\right)=\frac{1}{12}$

$\frac{1}{12}$

17. Determine the probability of choosing an even number that is not prime.

$\mathrm{P}\left(\mathrm{even} \cap \mathrm{prime}’\right)=\frac{6}{12}$

$\frac{1}{2}$

18. Determine the probability of choosing a number that is not even and not prime.

$\mathrm{P}\left(\mathrm{even}’ \cap \mathrm{prime}’\right)=\frac{2}{12}$

$\frac{1}{6}$

19. Determine the percentage of associate degree colleges in Maine.

Associate college row: $3.33\%+23.33\%$

26.7%

20. Determine the number of public associate degree colleges.

$$\begin{gathered} 23.33\% \mathrm{of} 30 \mathrm{colleges} \\ (0.2333)\left(30\right) \end{gathered}$$

7 public associate degree colleges

21. Determine the percentage of colleges that are non-associate degree colleges.

$50\%+23.33\%$

73.33%

22. Determine the number of private, non-associate colleges.

$$\begin{gathered} 50\% \mathrm{of} 30 \mathrm{colleges} \\ (0.5)\left(30\right) \end{gathered}$$

15 colleges are private, non-associate degree colleges.

23. Explain if this data represents mutually exclusive or inclusive events.

This represents inclusive events because there is an intersection between any two subsets.

24. If one college were randomly selected, which one is the least likely to be selected? Explain.

The least likely to be selected is the private associate college because only 3.33% of colleges have this degree program.