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# Proving independent random variables are almost deterministic watch

1. If X and Y are independent random variables, P(X + Y = c) = 1 how can I prove that X and Y are both almost deterministic random variables (so P(X = a) = P(Y = b) = 1)
a, b and c are all real constants
2. (Original post by Bruce Harrisface)
If X and Y are independent random variables, P(X + Y = c) = 1 how can I prove that X and Y are both almost deterministic random variables (so P(X = a) = P(Y = b) = 1)
a, b and c are all real constants
Have a think about the events

and

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