Hello Im getting back into statistics but I am a little rust

Hello. I\'m getting back into statistics, but I am a little rusty with it at the moment. I have a problem that I would like help with here:
A professor that makes decisions subjectively assigned the following probabilities to the four outcomes of an
experiment: P(E1) = .10, P(E2) = .15, P(E3) = .40, and P(E4) = .20. Would these probability
assignments be considered valid? Explain your answer.

Solution

If this is an appropriate probability distirbution, their probabilities must all add up to 1.

Thus,

P(E1) + P(E2) + P(E3) + P(E4) = 0.10 + 0.15 + 0.40 + 0.20 = 0.85

As they did not add up to 1, then NO, THESE ARE NOT VALID PROBABILITIES FOR A DISCRETE PROBABILITY DISTRIBUTION. [ANSWER]