Prove that 
Definitions:
College Professorship
A faculty position at a college or university, often including roles such as teaching, research, and administrative responsibilities.
Mutually Exclusive
A statistical term describing events that cannot occur at the same time, indicating no overlap in outcomes.
Joint Probability
The likelihood of two events happening at the same time.
Conditional Probability
The probability associated with an event under the condition that a separate event has already transpired.
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