Corrine needs to make a 2-digit code using the numbers 0–9 and the letters A–D. What is the complete sample space for this compound event? Show your work with a list, table, or tree diagram.
Sure! Here is the complete list without any dot dot dots:
00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 0A, 0B, 0C, 0D, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2A, 2B, 2C, 2D, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 3A, 3B, 3C, 3D, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 4A, 4B, 4C, 4D, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 5A, 5B, 5C, 5D, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 6A, 6B, 6C, 6D, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 7A, 7B, 7C, 7D, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 8A, 8B, 8C, 8D, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 9A, 9B, 9C, 9D.
The sample space for this compound event consists of all possible 2-digit codes using the numbers 0–9 and the letters A–D.
To create a list of the sample space, we can simply list all the possible combinations:
00, 01, 02, 03, ..., 09, 0A, 0B, 0C, 0D,
10, 11, 12, 13, ..., 19, 1A, 1B, 1C, 1D,
20, 21, 22, 23, ..., 29, 2A, 2B, 2C, 2D,
30, 31, 32, 33, ..., 39, 3A, 3B, 3C, 3D,
40, 41, 42, 43, ..., 49, 4A, 4B, 4C, 4D,
50, 51, 52, 53, ..., 59, 5A, 5B, 5C, 5D,
60, 61, 62, 63, ..., 69, 6A, 6B, 6C, 6D,
70, 71, 72, 73, ..., 79, 7A, 7B, 7C, 7D,
80, 81, 82, 83, ..., 89, 8A, 8B, 8C, 8D,
90, 91, 92, 93, ..., 99, 9A, 9B, 9C, 9D.
Therefore, the complete sample space for this compound event is:
{00, 01, 02, 03, ..., 09, 0A, 0B, 0C, 0D,
10, 11, 12, 13, ..., 19, 1A, 1B, 1C, 1D,
20, 21, 22, 23, ..., 29, 2A, 2B, 2C, 2D,
30, 31, 32, 33, ..., 39, 3A, 3B, 3C, 3D,
40, 41, 42, 43, ..., 49, 4A, 4B, 4C, 4D,
50, 51, 52, 53, ..., 59, 5A, 5B, 5C, 5D,
60, 61, 62, 63, ..., 69, 6A, 6B, 6C, 6D,
70, 71, 72, 73, ..., 79, 7A, 7B, 7C, 7D,
80, 81, 82, 83, ..., 89, 8A, 8B, 8C, 8D,
90, 91, 92, 93, ..., 99, 9A, 9B, 9C, 9D}.