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How the Monty Hall problem is similar to the false discovery rate in high-throughput data analysis

Nature Biotechnology volume 41, pages 754–755 (2023)Cite this article

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The Monty Hall problem is arguably one of the most well-known probability problems in the public domain1,2. The problem was named after Monty Hall, the host of the American television game show Let’s Make a Deal. The game has three doors, with a car behind one door and a goat behind each of the other two doors. The contestant does not know which door the car is behind and thus randomly chooses a door. This is where the situation becomes interesting. The host, who can see what is behind the two unchosen doors, opens one unchosen door with a goat behind it and asks the contestant if they would like to switch their already chosen door with the unopened unchosen door. The question is: would switching increase the contestant’s chance of winning?

The Monty Hall problem became famous as a brain teaser. An overwhelming majority of people’s first guess is that switching would not increase the chance of winning because it is impossible to be certain about which of the two unopened doors has the car behind it. However, the fact that the car can be behind either unopened door does not mean that the two unopened doors are equally likely to be hiding the car. What is the reason? The order of actions matters.

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Fig. 1: The order of actions matters in probability calculation: from the Monty Hall problem to the false discovery rate in high-throughput data analysis.

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Acknowledgements

The author appreciates comments and feedback from Wei Li at the University of California, Irvine, Chongzhi Zang at the University of Virginia, and the author’s PhD student Guanao Yan and postdoc Xinzhou Ge at UCLA. The author was supported by the following grants: National Science Foundation DBI-1846216 and DMS-2113754, NIH/NIGMS R35GM140888, a Johnson & Johnson WiSTEM2D Award, Sloan Research Fellowship, UCLA David Geffen School of Medicine W. M. Keck Foundation Junior Faculty Award, and the Chan-Zuckerberg Initiative Single-Cell Biology Data Insights Grant. The author was a fellow at the Radcliffe Institute for Advanced Study at Harvard University in 2022–2023 while writing this paper.

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  1. Department of Statistics, University of California, Los Angeles, Los Angeles, CA, USA

    Jingyi Jessica Li

  2. Radcliffe Institute of Advanced Study, Harvard University, Cambridge, MA, USA

    Jingyi Jessica Li

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Correspondence to Jingyi Jessica Li.

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Li, J.J. How the Monty Hall problem is similar to the false discovery rate in high-throughput data analysis. Nat Biotechnol 41, 754–755 (2023). https://doi.org/10.1038/s41587-023-01794-9

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