I have a question on Actex Prob Set 4, #12. X1 and X2 are 2 indep. random variables, but they have the same density function

f(x) = 2x for 0<x<1, 0 elsewhere. Find the probability that the max of X1 and X2 is at least .5.

The solution says P[Max{X1,X2}>=.5]=1-P[(X1<.5) and (X2<.5)]

Why can't you just evaluate P[(X1>.5) and (X2>.5)]? I don't have a complete understanding of Min/Max problems and Order Statatisics, so if you have any kind of explanation, I'd appreciate it!

f(x) = 2x for 0<x<1, 0 elsewhere. Find the probability that the max of X1 and X2 is at least .5.

The solution says P[Max{X1,X2}>=.5]=1-P[(X1<.5) and (X2<.5)]

Why can't you just evaluate P[(X1>.5) and (X2>.5)]? I don't have a complete understanding of Min/Max problems and Order Statatisics, so if you have any kind of explanation, I'd appreciate it!

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