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$X$ follows a continuous uniform distribution on $[0,3]$.$Y$ follows a discrete uniform distribution on $\{1,2,3\}$ Calculate the probability that $X<Y$.

Can we compare probability a continuous random variable with a discrete random variable? Do they have joint distribution? I tried to use the concept of joint distribution to solve this problem, Like drawing a pic and calculate the area.

What kind concept that I should use to solve this problem?

Thanks for the helps!

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Try using the law of total probability: $P(X<Y) = \sum_{i=1}^3 P(X<Y\cap Y=i) = \sum_{i=1}^3 P(X<Y| Y=i)P(Y=i)$.

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