45-733 PROBABILITY AND STATISTICS I


Answer to Problem 4


Let X = the number of times face 1 appears. Then

P(X = 1| X ³ 1) = P(X = 1 Ç X ³ 1)/P(X ³ 1) = P(X = 1)/[1 - P(X = 0)]

P(X = 0) = (5/6)3
P(X = 1) = (3 choose 1)*(1/6)*(5/6)2 Hence 

                            æ3ö 1æ5ö2
                            ç ÷ -ç-÷
                            è1ø 6è6ø
         P(X = 1|X ³ 1 ) = ----------
                                æ5ö3
                            1 - ç-÷
                                è6ø