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 conpound event? show you work with a list table or tree diagram.
To find the complete sample space for creating a 2-digit code using numbers 0-9 and letters a-d, we will create a list table.
Possible numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Possible letters: a, b, c, d
We will list all possible combinations using the digits from 00 to 99, where the first digit represents the tens place, and the second digit represents the ones place.
00 01 02 03 04 05 06 07 08 09
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
Now we will add the possible letters to each number to create all possible combinations:
00a 00b 00c 00d
01a 01b 01c 01d
02a 02b 02c 02d
03a 03b 03c 03d
04a 04b 04c 04d
05a 05b 05c 05d
06a 06b 06c 06d
07a 07b 07c 07d
08a 08b 08c 08d
09a 09b 09c 09d
10a 10b 10c 10d
11a 11b 11c 11d
12a 12b 12c 12d
13a 13b 13c 13d
...
99a 99b 99c 99d
The complete sample space for creating a 2-digit code using the numbers 0-9 and the letters a-d is:
00a, 00b, 00c, 00d, 01a, 01b, 01c, 01d, 02a, 02b, 02c, 02d, 03a, 03b, 03c, 03d, 04a, 04b, 04c, 04d, 05a, 05b, 05c, 05d, 06a, 06b, 06c, 06d, 07a, 07b, 07c, 07d, 08a, 08b, 08c, 08d, 09a, 09b, 09c, 09d, 10a, 10b, 10c, 10d, 11a, 11b, 11c, 11d, 12a, 12b, 12c, 12d, 13a, 13b, 13c, 13d, ..., 99a, 99b, 99c, 99d.