A electrician has on hand two boxes of capacitors with five

A electrician has on hand two boxes of capacitors, with five capacitor in each box. The capacitors in the first box are labeled 10 farad, but in fact their capacitance are 9, 10, 11, 12, and 13 farads. The capacitors in the second box are labeled 20 farads, but in fact their capacitance are 18, 19, 20, 21, and 22 farads. The Electrician chooses one capacitor from each box and determines the resistance of each. Let A be the event that the first capacitor has a capacitance greater than 11, let B be the event that the second capacitor has a capacitance less than 20, and let C be the event that the sum of the capacitance is equal to 30. List the sample space for this experiment, and specify the subsets corresponding to the events A, B, and C.

Solution

Sample space

{918,919,920,921.922,1018,1019.1020,1021,1022,1118,1119,1120,1121,1122,1218,1219,1220,1221,1222,1318,1319,1320,1321,1322}

A = { 1218,1219,1220,1221,1222,1318,1319,1320,1321,1322}

B = { 918,919,1018,1019,1118,1119,1218,1219,1318,1319}

C = { 921, 1020,1119,1218}