Practice 2 Solutions

1. Why is the probability of any event between zero and one?

Sample: Probability is a measure of how likely an event is to occur. The likelihood of an event cannot be less than 0 (not possible) or greater than 1 (completely certain).

2. What is the complement of an event?

Sample: A complement to an event is all of the events that are not the event.

3. P(5)

Total event: 1

Total outcomes: 9

$\mathrm{P}\left(5\right)=\frac{1}{9}$

4. P(even)

Even numbers: 2, 4, 6, 8

Total events: 4

Total outcomes: 9

$\mathrm{P}\left(\mathrm{even}\right)=\frac{4}{9}$

5. P(odd)

P(odd) is the complement of P(even)

$1–\frac{4}{9}=\frac{5}{9}$

$\mathrm{P}\left(\mathrm{odd}\right)=\frac{5}{9}$

6. P(multiple of 3)

Multiples of 3: 3, 6, 9

Total events: 3

Total outcomes: 9

$\mathrm{P}\left(\mathrm{multiple} \mathrm{of} 3\right)=\frac{3}{9}$

$\mathrm{P}\left(\mathrm{multiple} \mathrm{of} 3\right)=\frac{1}{3}$

7. Determine the probability of rolling a sum of 11.

$$\begin{gathered} \mathrm{Sum} \mathrm{of} 11: 5 \mathrm{and} 6, 6 \mathrm{and} 5=2 \\ \mathrm{Total} \mathrm{outcomes}:\hspace{0.17em}6·6=36 \\ \mathrm{P}\left(\mathrm{sum} \mathrm{of} 11\right)=\frac{2}{36} \end{gathered}$$

$\mathrm{P}\left(\mathrm{sum} \mathrm{of} 11\right)=\frac{1}{18}$

8. Determine the probability of rolling a sum less than 5.

Rolls less than 5: 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 2 and 2

Total events: 6

Total outcomes: 36

$\mathrm{P}\left(\mathrm{less} \mathrm{than} 5\right)=\frac{6}{36}$

$\mathrm{P}\left(\mathrm{less} \mathrm{than} 5\right)=\frac{1}{6}$

9. Determine the probability of rolling a sum greater than 12.

Sample: There are no numbers greater than 12.

Sample: There is a zero probability of rolling a number greater than 12.

10. Determine the probability of rolling an even sum.

Even numbers: 2, 4, 6, 8, 10, 12

Total even sum: 18

Total outcomes: 36

$\mathrm{P}\left(\mathrm{even}\right)=\frac{18}{36}$

$\mathrm{P}\left(\mathrm{even}\right)=\frac{1}{2}$

11. Determine the probability of drawing a card with a two on it.

Total events: 4

Total outcomes: 52

$\mathrm{P}\left(2\right)=\frac{4}{52}$

$\mathrm{P}\left(2\right)=\frac{1}{13}$

12. Determine the probability of selecting a face card (jack, queen, king).

Total events: 3 cards in each of 4 suits = 12

Total outcomes: 52

$\mathrm{P}\left(\mathrm{face} \mathrm{card}\right)=\frac{12}{52}$

$\mathrm{P}\left(\mathrm{face} \mathrm{card}\right)=\frac{3}{13}$

13. Find the experimental probability as a decimal for each letter on the spinner.

Total: $65+39+28+68=200$

$\mathrm{P}\left(\mathrm{M}\right)=0.33, \mathrm{P}\left(\mathrm{A}\right)=0.20, \mathrm{P}\left(\mathrm{T}\right)=0.14, \mathrm{P}\left(\mathrm{H}\right)=0.34$

14. Determine the most likely letter (event) to occur according to the chart.

The letter H has the highest experimental probability (34%) of being stopped on, making it the most likely to be selected.

15. Determine the least likely letter (event) to occur according to the chart.

The letter T has the lowest experimental probability (14%) of being stopped on, which makes it the least likely to be selected.

16. Using the spinner, estimate the theoretical probability for stopping on each letter. Explain.

Sample: The spinner shows four equal-sized wedges, giving a 25% chance of each occurring.

17. Does the image of the spinner match the information from the experiment? Explain.

Sample: No, the spinner shown would result in each letter being equally likely. The experiment has 200 trials, so either the spinner is unfair, or a different spinner was used for the actual experiment with differently sized wedges.

18. Reese selects an apple cinnamon packet.

$$\begin{gathered} \mathrm{Total}: 6+8+8+2=24 \\ \mathrm{P}\left(\mathrm{A}\right)=\frac{6}{24}=\frac{1}{4} \end{gathered}$$

Unlikely

Apple cinnamon has a 25% chance of being selected randomly.

19. Reese selects a banana packet.

Will never happen

There are no banana packets.

20. Reese selects a blueberry or a strawberry packet.

$$\begin{gathered} \mathrm{Total}: 6+8+8+2=24 \\ \mathrm{P}(\mathrm{M} \mathrm{or} \mathrm{S})=\frac{8+8}{24}=\frac{16}{24}=\frac{2}{3} \end{gathered}$$

Likely

Blueberry and strawberry are the most common, and together are about 66% of the box.