Enhancing the validity of probability prompts using four generative artificial intelligence tools

Ayşe Fethiye Gemci
James Madison University
Amanda Gantt Sawyer
James Madison University
Haley Smiley
James Madison University
Richard Busi
James Madison University
Juliana Galano
James Madison University

Article ID: 4266

Keywords: generative artificial intelligence; probability; accuracy of artificial intelligence

Abstract

Generative Artificial Intelligence (genAI) has become a large influence on students and teachers in the mathematics classroom. Specifically, researchers found that genAI tools could solve probability questions such as “What is the probability of drawing the Queen of Hearts from a standard deck of playing cards on the first try?” These researchers also stated that the genAI tools could not be trusted when solving, “Three cards are lying face down in front of me. Two are face cards, and there are no spades. No card is next to a card of the same color. What are the odds that the card on the left is the Queen of Hearts?” However, it is unclear whether that statement is true. Thus, we verified these findings by investigating four genAI tools (ChatGPT, Gemini, Co-Pilot, and Claude AI) on their ability to complete the identified probability task to determine when genAI can be trusted to perform probability calculation. Using the results of this investigation, we examined these genAI models using their responses and the predictions made by the genAI trainer. The investigation implies that developing mathematical validity requires intentional instruction, including teaching students how to compare genAI’s explanations, conducting GenAI Triangulation Process, cross-checking results using independent methods or alternative tools, and justifying whether an answer is mathematically sound.

Published

2026-10-20

How to Cite

Gemci, A. F., Sawyer, A. G., Smiley, H., Busi, R., & Galano, J. (2026). Enhancing the validity of probability prompts using four generative artificial intelligence tools. Computing and Artificial Intelligence, 4(3). https://doi.org/10.59400/cai4266

Download Citation

Issue

Vol. 4 No. 3 (2026)

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

[1]Ding, L., Li, T., Jiang, S., & Gapud, A. (2023). Students’ perceptions of using ChatGPT in a physics class as a virtual tutor. International Journal of Educational Technology in Higher Education, 20(1), 63.

[2]Sawyer, A. G. (2024). Artificial intelligence chatbot as a mathematics curriculum developer: Discovering preservice teachers’ overconfidence in ChatGPT. International Journal on Responsibility, 7(1), Article 1. doi:10.62365/2576-0955.1106

[3]Marcus, G. (2023). “Math is hard” – If you are an LLM, why does that matter? Marcus on AI. Substack. https://garymarcus.substack.com/p/math-is-hard-if-you-are-an-llm-and

[4]Sawyer, A. G., Christian, M., & Sutherland, P. (2026). Educators' discussions with a generative artificial intelligence trainer. Innovations in Pedagogy and Technology, 2(3).

[5]Stryker, C., & Kavlakoglu, E. (2024). What is artificial intelligence? IBM. https://www.ibm.com/think/topics/artificial-intelligence

[6]Sharma, N. (2024). Generative AI, conversion AI, and chatbot - A breakdown. Nimble App Genies. https://www.nimbleappgenie.com/blogs/generative-ai-vs-conversational-ai-vs-chatbot/

[7]Kanbach, D. K., Heiduk, L., Blueher, G., Schreiter, M., & Lahmann, A. (2024). The GenAI is out of the bottle: Generative artificial intelligence from a business model innovation perspective. Review of Managerial Science, 18(4), 1189–1220.

[8]Stripling, J. (2025, November 19). Using AI without (really) cheating. Chronicle. https://www.chronicle.com/podcast/college-matters-from-the-chronicle/using-ai-without-really-cheating

[9]Wu, G. (2023, September 17). 8 big problems with OpenAI's ChatGPT. Make Use Of. https://www.makeuseof.com/openai-chatgpt-biggest-probelms/

[10]Sawyer, A., & Aga, Z. (2024). Counterexamples to demonstrate artificial intelligence chatbots’ lack of knowledge in the mathematics education classroom. AMTE Connections.

[11]https://amte.net/connections/2024/05/connections-thematic-articles-artificial-intelligence-mathematics-teacher

[12]National Council of Teachers of Mathematics. (2024). NCTM releases new position statement on artificial intelligence and mathematics teaching. NCTM. https://www.nctm.org/News-and-Calendar/News/NCTM-News-Releases/NCTM-Releases-New-Position-Statement-on-Artificial-Intelligence-and-Mathematics-Teaching/

[13]Yoon, H., Hwang, J., Lee, K., Roh, K. H., & Kwon, O. N. (2024). DynaMath: A dynamic visual benchmark for evaluating the mathematical reasoning robustness of vision language models. arXiv.

[14]U.S. Department of Education. (2025). Artificial intelligence (AI) guidance. USDOE. https://www.ed.gov/about/ed-overview/artificial-intelligence-ai-guidance

[15]The Guardian. (2025). Elon Musks xAI is accused of pollution over the Memphis supercomputer. The Guardian. https://www.theguardian.com/technology/2025/apr/24/elon-musk-xai-memphis

[16]Stahl, B. C. (2021). Ethical issues of AI. In Artificial Intelligence for a better future: An ecosystem perspective on the ethics ofAI and emerging digital technologies. Springer International Publishing, 35-53.

[17]Bastani, H., Bastani, O., Sungu, A., Ge, H., Kabakcı, O., & Mariman, R. (2024). Generative AI can harm learning. Atelier des Futurs, 1–59.

[18]Krutka, D. G., Heath, M. K., & Willet, K. B. S. (2019). Foregrounding technoethics: Toward critical perspectives in technology and teacher education. Journal of Technology and Teacher Education, 27(4), 555-574.

[19]Baum, J., & Villasenor, J. (2023). The politics of AI: ChatGPT and political bias. Brookings.

[20]https://www.brookings.edu/articles/the-politics-of-ai-chatgpt-and-political-bias

[21]Israel/OPT: Clock Tower X allegedly hired by Israeli government to create “pro-israel” content, training chatgpt and targeting Facebook, Instagram, TikTok and YouTube, Incl. cos. response and non-responses. Business and Human Rights Centre. (n.d.). https://www.business-humanrights.org/en/latest-news/israelopt-clock-tower-x-allegedly-hired-by-israeli-government-to-create-pro-israel-content-training-chatgpt-and-targeting-facebook-instagram-tiktok-youtube-incl-cos-response-and-non-responses/

[22]Murphy, R. F. (2019). Artificial intelligence applications to support K- 12 teachers and teaching. Rand Corporation, 10(1), 1-20.

[23]Future of Life Institute. (2025). AI safety index. Future of Life. https://futureoflife.org/wp-content/uploads/2025/07/FLI-AI-Safety-Index-Report-Summer-2025.pdf

[24]Korzynski, P., Mazurek, G., Krzypkowska, P., & Kurasinski, A. (2023). Artificial intelligence prompt engineering as a new digital competence: Analysis of generative AI technologies such as ChatGPT. Entrepreneurial Business and Economics Review, 11(3), 25-37.

[25]DAIR.AI. (2025). Elements of a prompt. Prompt Engineering Guide. https://www.promptingguide.ai/introduction/elements

[26]Han, B. (2023). 6 essential elements of AI prompt engineering: TCEPFT as BK Han’s mnemonic. Medium. https://medium.com/@BK.HAN/6-essential-elements-of-ai-prompt-engineering-tcepft-as-bk-hans-mnemonic-43e689f22ad8

[27]Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., ... & Amodei, D. (2020). Language models are few-shot learners. Advances in neural information processing systems, 33, 1877- 1901.

[28]Shin, T., Razeghi, Y., Iv, R. L. L., Wallace, E., & Singh, S. (2020, November). Autoprompt: Eliciting knowledge from language models with automatically generated prompts. In Proceedings of the 2020 conference on empirical methods in natural language processing (EMNLP) (pp. 4222-4235).

[29]Zamfirescu-Pereira, J. D., Wong, R. Y., Hartmann, B., & Yang, Q. (2023, April). Why Johnny can’t prompt: How non-AI experts try (and fail) to design LLM prompts. In Proceedings of the 2023 CHI conference on human factors in computing systems (pp. 1- 21).

[30]Mills, A. J., Durepos, G., & Wiebe, E. (Eds.). (2010). Exploratory case study. In Encyclopedia of Case Study Research (pp. 358–360). SAGE Publications.

[31]Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27–40.

[32]Titan Technology. (2025). Top 10 most used genAI tools in 2025. Titan Corporation. https://titancorpvn.com/insight/technology-insights/top-10-most-used-gen-ai-tools-in-2025

[33]Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage Publications.

[34]Xu, H., Chen, Y., Du, Y., Shao, N., Yanggang, W., Li, H., & Yang, Z. (2022, December). ZeroPrompt: Scaling prompt-based pretraining to 1,000 tasks improves zero-shot generalization. In Findings of the Association for Computational Linguistics: EMNLP 2022 (pp. 4235-4252).

[35]Langreo, L. (2024, October 24). Most teachers are not using AI. Here 's why. Education Week. https://www.edweek.org/technology/most-teachers-are-not-using-ai-heres-why/2024/01

[36]Jentoft, N., & Olsen, T. S. (2019). Against the flow in data collection: How data triangulation combined with a ‘slow’interview technique enriches data. Qualitative Social Work, 18(2), 179- 193.

Editor-in-Chief

Prof. Shaohua Wan
University of Electronic Science and Technology of China, China

eISSN

3029-2786

Publication Frequency

Quarterly (since 2025)

Indexing

All the publications will be archived by the PKP Preservation Network for long-term electronic preservation.

Authors are encouraged to self-archive the final version of their published articles into institutional repositories (such as those listed in the Directory of Open Access Repositories).

Authors are also encouraged to use the final PDF version published on the website of Academic Publishing.

Scilit Database (Switzerland)

Google Scholar

J-Gate

About the Publisher

Academic Publishing insists on taking academic exchange and publication as the main line, carrying out comprehensive management based on science and technology, and fully exploring excellent international publishing resources. Within 5 years, it will form a strategic framework and scale with science (S), technology (T), medicine (M), education (E), and humanities and arts (H) as the main publishing fields. Academic Publishing is headquartered in Singapore and based in Malaysia, with the United States and China providing the main scientific and academic resources. At the same time, it has established long-term good cooperative relations with other publishing companies, scientific research communities, and academic organizations in more than a dozen countries and regions. Academic Publishing uses English and Chinese as its main publishing languages, mainly publishing books, journals, and conference papers in print and online. The vast majority of publications follow the international open access policy, providing stable and long-term quality and professional publications. With the joint efforts of the expert team and our professional editorial team, our publications will gradually be indexed by international databases in stages to provide convenient and professional retrieval for various scholars. At the same time, manuscripts we accept will be subject to the peer review principle, and cutting-edge and innovative research articles will be preferentially accepted for peer reference and discussion. All kinds of our publications are welcome for peer to contribute, access, and download.

more

Volume Arrangement

2026

2025

2024

2023

Featured Articles

Identifying voices using convolution neural network models AlexNet and ResNet

Deep learning (DL) techniques which implement deep neural networks became popular due to the increase of high-performance computing facilities. DL achieves higher power and flexibility due to its ability to process many features when it deals with unstructured data. DL algorithm passes the data through several layers; each layer is capable of extracting features progressively and passes it to the next layer. Initial layers extract low-level features, and succeeding layers combine features to form a complete representation. This research attempts to utilize DL techniques for identifying sounds. The development in DL models has extensively covered classification and verification of objects through images. However, there have not been any notable findings concerning identification and verification of the voice of an individual from different other individuals using DL techniques. Hence, the proposed research aims to develop DL techniques capable of isolating the voice of an individual from a group of other sounds and classify them based on the use of convolutional neural networks models AlexNet and ResNet, that are used in voice identification. We achieved the classification accuracy of ResNet and AlexNet model for the problem of voice identification is 97.2039 % and 65.95% respectively, in which ResNet model achieves the best result.

Revolutionizing Neurosurgery and Neurology: The transformative impact of artificial intelligence in healthcare

The integration of artificial intelligence (AI) has brought about a paradigm shift in the landscape of Neurosurgery and Neurology, revolutionizing various facets of healthcare. This article meticulously explores seven pivotal dimensions where AI has made a substantial impact, reshaping the contours of patient care, diagnostics, and treatment modalities. AI’s exceptional precision in deciphering intricate medical imaging data expedites accurate diagnoses of neurological conditions. Harnessing patient-specific data and genetic information, AI facilitates the formulation of highly personalized treatment plans, promising more efficacious therapeutic interventions. The deployment of AI-powered robotic systems in neurosurgical procedures not only ensures surgical precision but also introduces remote capabilities, mitigating the potential for human error. Machine learning models, a core component of AI, play a crucial role in predicting disease progression, optimizing resource allocation, and elevating the overall quality of patient care. Wearable devices integrated with AI provide continuous monitoring of neurological parameters, empowering early intervention strategies for chronic conditions. AI’s prowess extends to drug discovery by scrutinizing extensive datasets, offering the prospect of groundbreaking therapies for neurological disorders. The realm of patient engagement witnesses a transformative impact through AI-driven chatbots and virtual assistants, fostering increased adherence to treatment plans. Looking ahead, the horizon of AI in Neurosurgery and Neurology holds promises of heightened personalization, augmented decision-making, early intervention, and the emergence of innovative treatment modalities. This narrative is one of optimism and collaboration, depicting a synergistic partnership between AI and healthcare professionals to propel the field forward and significantly enhance the lives of individuals grappling with neurological challenges. This article provides an encompassing view of AI’s transformative influence in Neurosurgery and Neurology, highlighting its potential to redefine the landscape of patient care and outcomes.

Enhancing user experience in large language models through human-centered design: Integrating theoretical insights with an experimental study to meet diverse software learning needs with a single document knowledge base

This paper begins with a theoretical exploration of the rise of large language models (LLMs) in Human-Computer Interaction (HCI), their impact on user experience (HX) and related challenges. It then discusses the benefits of Human-Centered Design (HCD) principles and the possibility of their application within LLMs, subsequently deriving six specific HCD guidelines for LLMs. Following this, a preliminary experiment is presented as an example to demonstrate how HCD principles can be employed to enhance user experience within GPT by using a single document input to GPT’s Knowledge base as new knowledge resource to control the interactions between GPT and users, aiming to meet the diverse needs of hypothetical software learners as much as possible. The experimental results demonstrate the effect of different elements’ forms and organizational methods in the document, as well as GPT’s relevant configurations, on the interaction effectiveness between GPT and software learners. A series of trials are conducted to explore better methods to realize text and image displaying, and jump action. Two template documents are compared in the aspects of the performances of the four interaction modes. Through continuous optimization, an improved version of the document was obtained to serve as a template for future use and research.

Clustering data analytics of urban land use for change detection

In this study, the author proposes and details a workflow for the spatial-temporal demarcation of urban areal features in 8 cities of Tamilnadu, India. During the inception phase, functional requirements and non-functional parameters are analyzed and designed, within a suitable pixel area and object-oriented derived paradigm. Land use categories are defined from OpenStreetMap (OSM) related works with the scope of conducting climate change, using multispectral sensors onboard Landsat series. Furthermore, we augment the bands dataset with Spatially Invariant Feature Transform (SIFT), Normalized Difference Vegetation Index (NDVI), Normalized Difference Built-Up Index (NDBI), Leaf Area Index (LAI), and Texture base indices, as a means of spatially integrating auto-covariance to stationarity patterns. In doing so, change detection can be pursuit by scaling up the segmentation of regional/zonal boundaries in a multi-dimensional environment, with the aid of Wide Area Networks (WAN) cluster computers such as the BEOWULF/Google Earth Engine clusters. GeoAnalytical measures are analyzed in the design of local and zonal spatial models (GRID, RASTER, DEM, IMAGE COLLECTION). Finally, multi variate geostatistical works are ensued for precision and recall in predictive data analytics. The author proposes reusing machine learning tools (filtering by attribute-based indexing in PaaS clouds) for pattern recognition and visualization of features and feature collection.

Application of computer vision in livestock and crop production—A review

Nowadays, it is a challenge for farmers to produce healthier food for the world population and save land resources. Recently, the integration of computer vision technology in field and crop production ushered in a new era of innovation and efficiency. Computer vision, a subfield of artificial intelligence, leverages image and video analysis to extract meaningful information from visual data. In agriculture, this technology is being utilized for tasks ranging from disease detection and yield prediction to animal health monitoring and quality control. By employing various imaging techniques, such as drones, satellites, and specialized cameras, computer vision systems are able to assess the health and growth of crops and livestock with unprecedented accuracy. The review is divided into two parts: Livestock and Crop Production giving the overview of the application of computer vision applications within agriculture, highlighting its role in optimizing farming practices and enhancing agricultural productivity.