[EDIT] The last version of MAMP with the last version of OSX Yosemite works fine.
I installed the beta of Yosemite two month ago, no problem with MAMP. With the last release of OSX, Apache and MySQL did not work.
I found a solution for Apache by using the default port 80 and renaming the file envvars to _envvars in Applications/MAMP/Library/bin but have not been able to solve the problem with MySQL.
The issue is usually due to another MySQL service running on the same port. The easiest solution is to kill all MySQL processes and restart MAMP. On macOS, you can do this using the Activity Monitor, which you'll find in the Utilities folder on your computer.
Support Ending December 31, 2019 In keeping with Apple's release cycle, macOS 10.10 Yosemite is no longer receiving security updates as of November of 2015. Our latest fully-supported operating system is macOS Mojave (10.14).
Per the Knowledge Base at MAMP for "Apache will not start - Yosemite Beta":
Rename the file
envvars
located in/Applications/MAMP/Library/bin
into_envvars
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