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A problem in Shanghai mathematics college entrance examination
You just need to exclude those who have taken the same course.

Choose two, and the probability that they are the same course is

( 15/50)*( 14/49) + (35/50)*(34/49)

= ( 15* 14+35*34)/50/49

= 1400/50/49

= 28/49 = 4/7

So the different probability is 1-4/7=3/7.