Question
PART C:
#11-15
You are going to host a party and serve ice cream to your attendees. You have decided to give choices, you will offer either a sugar or waffle cone and a choice of chocolate, vanilla, or strawberry ice cream.
Double-click the drawing to fill in the tree diagram for the situation above (9 points) and then answer the following questions ( 3 points each)
11.)
12.) How many total combinations are possible?
13.) If you were to get a scoop/cone at random, what is the likelihood of getting a chocolate waffle cone?
14.) If you were to get a scoop/cone at random, what is the likelihood of getting a waffle cone?
15.) If you were to get a scoop/cone at random, what is the likelihood of getting a vanilla cone?
#11-15
You are going to host a party and serve ice cream to your attendees. You have decided to give choices, you will offer either a sugar or waffle cone and a choice of chocolate, vanilla, or strawberry ice cream.
Double-click the drawing to fill in the tree diagram for the situation above (9 points) and then answer the following questions ( 3 points each)
11.)
12.) How many total combinations are possible?
13.) If you were to get a scoop/cone at random, what is the likelihood of getting a chocolate waffle cone?
14.) If you were to get a scoop/cone at random, what is the likelihood of getting a waffle cone?
15.) If you were to get a scoop/cone at random, what is the likelihood of getting a vanilla cone?
Answers
GPT-4o mini
To visualize the options available for the ice cream party, we can create a tree diagram that represents the different combinations of cone types and ice cream flavors.
**Tree Diagram:**
1. Cone Type:
- Sugar Cone
- Chocolate Ice Cream
- Vanilla Ice Cream
- Strawberry Ice Cream
- Waffle Cone
- Chocolate Ice Cream
- Vanilla Ice Cream
- Strawberry Ice Cream
From this, we can derive the combinations:
- **Sugar Cone:**
- Chocolate
- Vanilla
- Strawberry
- **Waffle Cone:**
- Chocolate
- Vanilla
- Strawberry
**Combinations:**
1. Sugar Cone with Chocolate Ice Cream
2. Sugar Cone with Vanilla Ice Cream
3. Sugar Cone with Strawberry Ice Cream
4. Waffle Cone with Chocolate Ice Cream
5. Waffle Cone with Vanilla Ice Cream
6. Waffle Cone with Strawberry Ice Cream
### Questions:
**11.) How many total combinations are possible?**
There are 2 types of cones (sugar or waffle) and 3 flavors of ice cream (chocolate, vanilla, or strawberry).
Total combinations = Number of Cone Types × Number of Ice Cream Flavors = 2 × 3 = **6** combinations.
---
**12.) If you were to get a scoop/cone at random, what is the likelihood of getting a chocolate waffle cone?**
There is 1 combination that results in a chocolate waffle cone (Waffle Cone with Chocolate Ice Cream) out of the total 6 combinations.
Likelihood = Number of favorable outcomes / Total outcomes = 1/6 = **1/6** or approximately **0.167** (16.7%).
---
**13.) If you were to get a scoop/cone at random, what is the likelihood of getting a waffle cone?**
There are 3 combinations with a waffle cone (Waffle Cone with Chocolate, Vanilla, and Strawberry Ice Cream) out of the total 6 combinations.
Likelihood = Number of favorable outcomes / Total outcomes = 3/6 = **1/2** or 50%.
---
**14.) If you were to get a scoop/cone at random, what is the likelihood of getting a vanilla cone?**
There are 2 combinations with vanilla (Sugar Cone with Vanilla, Waffle Cone with Vanilla) out of the total 6 combinations.
Likelihood = Number of favorable outcomes / Total outcomes = 2/6 = **1/3** or approximately **0.333** (33.3%).
---
**15.) If you were to get a scoop/cone at random, what is the likelihood of getting a strawberry cone?**
Similar to vanilla, there are also 2 combinations with strawberry (Sugar Cone with Strawberry, Waffle Cone with Strawberry) out of the total 6 combinations.
Likelihood = Number of favorable outcomes / Total outcomes = 2/6 = **1/3** or approximately **0.333** (33.3%).
To summarize:
- Total combinations: **6**
- Likelihood of chocolate waffle cone: **1/6**
- Likelihood of getting a waffle cone: **1/2**
- Likelihood of getting a vanilla cone: **1/3**
- Likelihood of getting a strawberry cone: **1/3**
**Tree Diagram:**
1. Cone Type:
- Sugar Cone
- Chocolate Ice Cream
- Vanilla Ice Cream
- Strawberry Ice Cream
- Waffle Cone
- Chocolate Ice Cream
- Vanilla Ice Cream
- Strawberry Ice Cream
From this, we can derive the combinations:
- **Sugar Cone:**
- Chocolate
- Vanilla
- Strawberry
- **Waffle Cone:**
- Chocolate
- Vanilla
- Strawberry
**Combinations:**
1. Sugar Cone with Chocolate Ice Cream
2. Sugar Cone with Vanilla Ice Cream
3. Sugar Cone with Strawberry Ice Cream
4. Waffle Cone with Chocolate Ice Cream
5. Waffle Cone with Vanilla Ice Cream
6. Waffle Cone with Strawberry Ice Cream
### Questions:
**11.) How many total combinations are possible?**
There are 2 types of cones (sugar or waffle) and 3 flavors of ice cream (chocolate, vanilla, or strawberry).
Total combinations = Number of Cone Types × Number of Ice Cream Flavors = 2 × 3 = **6** combinations.
---
**12.) If you were to get a scoop/cone at random, what is the likelihood of getting a chocolate waffle cone?**
There is 1 combination that results in a chocolate waffle cone (Waffle Cone with Chocolate Ice Cream) out of the total 6 combinations.
Likelihood = Number of favorable outcomes / Total outcomes = 1/6 = **1/6** or approximately **0.167** (16.7%).
---
**13.) If you were to get a scoop/cone at random, what is the likelihood of getting a waffle cone?**
There are 3 combinations with a waffle cone (Waffle Cone with Chocolate, Vanilla, and Strawberry Ice Cream) out of the total 6 combinations.
Likelihood = Number of favorable outcomes / Total outcomes = 3/6 = **1/2** or 50%.
---
**14.) If you were to get a scoop/cone at random, what is the likelihood of getting a vanilla cone?**
There are 2 combinations with vanilla (Sugar Cone with Vanilla, Waffle Cone with Vanilla) out of the total 6 combinations.
Likelihood = Number of favorable outcomes / Total outcomes = 2/6 = **1/3** or approximately **0.333** (33.3%).
---
**15.) If you were to get a scoop/cone at random, what is the likelihood of getting a strawberry cone?**
Similar to vanilla, there are also 2 combinations with strawberry (Sugar Cone with Strawberry, Waffle Cone with Strawberry) out of the total 6 combinations.
Likelihood = Number of favorable outcomes / Total outcomes = 2/6 = **1/3** or approximately **0.333** (33.3%).
To summarize:
- Total combinations: **6**
- Likelihood of chocolate waffle cone: **1/6**
- Likelihood of getting a waffle cone: **1/2**
- Likelihood of getting a vanilla cone: **1/3**
- Likelihood of getting a strawberry cone: **1/3**