# Finding probability of a minimum

let X1 and X2 be two randomly selected random variables from the same discrete distribution. Let Y=min(X1,X2). Find P(Y=1)

according to the book. P(Y=1)=P[(X1=1)and(X2>=1)]+P[(X2=1)and(X1>=2)]

I don't understand why is the asymmetry is even possible. The way I look at it, it's
P(Y=1)=P[(X1=1)and(X2>1)]+P[(X2=1)and(X1>1)]

Stephen Tashi