1. A coin is tossed then S1 = {H, T}
A die is rolled then S2 = {1, 2, 3, 4, 5, 6}
Hence sample space
S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}.
2. A coin is tossed then S1 = {H, T}
A die is rolled then S2 = {1, 2, 3, 4, 5, 6}
Hence sample space S = {H1, H2, H3,H4, H5,H6, T}
3. Let B1, B2 denote the boys and G1, G2 girls in room X, B1 denote the boys and G3, G4, G5 girls in room Y. Hence sample space
S = {XB1, XB2, XG1, XG2, YB1, YG3, XG4, XG5}
4. Three die are R,W, and B, then S1 = {R, W, B)
A die is rolled then S2 = {1, 2, 3, 4, 5, 6}
Hence sample space S = {R1, R2, R3, R4, R5, R6, W1, W2, W3, W4, W5, W6, B1, B2, B3, B4, B5, B6}
5. A coin is tossed then S1 = {H, T}
A coin tossed again then S2 = {H, T}
A die is rolled then S3 = {1, 2, 3, 4, 5, 6}
Hence sample space
S = {HH, HT, T1, T2, T3, T4, T5, T6}
6. A coin is tossed then S1 = {H, T}
When the coin shows T, then there is no action. When the coin shows H, a die is thrown
S2 = {1, 2, 3, 4, 5, 6}
When the die shows {1, 3, 5}, then there is no action.
When the die shows {2, 4, 6}, then a die is thrown again.
Hence;
S = {T, H1, H3, H5, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H45, H46,H61, H62, H63, H64, H65, H66}.