Question

A chance experiment consists of drawing a raffle ticket from a box of tickets numbered 1, · · · , 40. Let Ω represent the sample space for this experiment. Since we select one ticket at random, Ω is an equally-likely sample space. Let E1,··· ,E8 where Ei ⊂ Ω be a partition of Ω defined as: E1 = {1,3,5,7,9}, E2 = {11,13,15,17,19}, E3 = {21,23,25,27,29}, E4 = {31,33,35,37,39}, E5 = {2,4,6,8}, E6 = {10,12,14,16,18}, E7 = {20,22,24,26,28}, E8 = {30, 32, 34, 36, 38, 40}. Let F ⊂ Ω be the set of factors of 36. Find P (F ) using the Law of Total Probability. (Show all your work.)

Answer 1

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

So we have the following intersections possible

Where

Thus, using the Law of Total Probability we get