Is probability theory useful in electrical engineering
Probability theory is very relevant to Electrical Engineering -- in fact several universities have courses just on this topic, such as University of Utah's ECE 3530/CS 3130 - Engineering Probability and Statistics and USC's EE503 Probability for Electrical and Computer Engineers.  Take a look at the syllabi for these courses and you will get a feel for the many different topics covered.

Probability is particularly relevant in the area of quality engineering, and being able to design reliable circuits where you have to take into account the tolerance of various components, and the predicted lifetimes. What is the mean-time-to-failure (MTTF) of your system?

Where can you get by with a 20% tolerance capacitor instead of a more expensive 5% one?  In a recent design of mine, I had to use a 0.1% resistor in a current sensor instead of the usual 1% resistors I always use.

I have used a Poisson distribution to predict the maximum amount of memory needed so I would have adequate buffers to handle peak incoming traffic in an embedded system based on the expected average traffic entering the system.

Communications theory and error correction are all about probability and statistics, where the maximum amount of information is jammed into the smallest amount of bandwidth, while dealing with possibly very noisy channels.