Monday Tuesday Wednesday
CS(0.4) Let cs1=Studying computer science on Monday,cs2=studying computer science on Tuesday
CS(0.4) cs3=studying computer science on Wednesday,math1=studying math on Monday
Math(0.6) math2=studying math on Tuesday,math3=studying math on Wednesday
CS Now P(studying computer science on Wednesday given that studying cs on Monday)
CS(0.4)
Math(0.6) ={P(cs1∩cs2∩cs3)+P(cs1∩math2∩cs3)}/P(cs1)
Math(0.6) ={P(cs3|cs1∩cs2)*P(cs1∩cs2)+P(cs3|cs1∩math2)*P(cs1∩math2)}/P(cs1)
={P(cs3|cs1∩cs2)*P(cs2|cs1)*P(cs1)+P(cs3|cs1∩math2)*P(math2|cs1)P(cs1)}/P(cs1)
= P(cs3|cs1∩cs2)*P(cs2|cs1)+P(cs3|cs1∩math2)*P(math2|cs1)
CS(0.4) =0.4*0.4+0.4*0.6
CS(0.4) =0.4 (C)
Math(0.6)
Math
CS(0.4)
Math(0.6)
Math(0.6)