uniform distribution

Question

x1 x2 x3 are  three independent random variables distributed uniformly on [0,1].Find probability that P(X1 is largest )

Comments

I m getting 1/12.

Answer 1

probability is 1/3..

Solution:- there are 6 cases P(x1>x2>x3), P(x1>x3>x2), P(x2>x1>x3), P(x2>x3>x1), P(x3>x2>x1), P(x3>x1>x2).

All cases are equally likely and hence P(x1) being largest is P(x1>x2>x3) or P(x1>x3>x2).

Hence, P(x1 being largest)=2/6=1/3