Problem Set 9 What is the probability that there is a mine at the square marked x? Solution. If there is a mine at square then the state of all the other squares next to numbers is complete determined and 6 of the other 49 squares are mined. Therefore, the probability that r is mined is Pr (x mined E)=Pr(x mined E)=(6)=0. 0175 Pr(e) (d) What is the probability that there is a mine at the square marked y? Solution. If there is a mine at square y, then two of the three squares marked e are mined as well as 7 of the remaining 49 squares. Thus, the probability that there is a mine at y is Pr(y mined e Pr(y minedne) 2) 0.324 Pr(e Thus, a mine at y is 18+ times more likely than a mine r (You may leave your answers in symbolic form, but the numerical answers are surely more interesting!)� � � �� � Problem Set 9 11 x XX y XXX  XXXz 9 1 1 3 What is the probability that there is a mine at the square marked x? Solution. If there is a mine at square x, then the state of all the other squares next to numbers is complete determined and 6 of the other 49 squares are mined. Therefore, the probability that x is mined is: 49 Pr (x mined E) = Pr (x mined ∩ E) 6 Pr (E) |E| | = = 0.0175 . . . (d) What is the probability that there is a mine at the square marked y? Solution. If there is a mine at square y, then two of the three squares marked e are mined as well as 7 of the remaining 49 squares. Thus, the probability that there is a mine at y is: 3 49 2 Pr (y mined | E) = Pr (y mined ∩ E) 7 = = 0.324 . . . Pr (E) |E| Thus, a mine at y is 18+ times more likely than a mine x! (You may leave your answers in symbolic form, but the numerical answers are surely more interesting!)