To determine the sample space for the numbers on a phone, we need to consider the typical layout of a modern telephone keypad. Here is the breakdown of the different options provided:
a) [tex]\(\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , \#\}\)[/tex]
b) [tex]\(\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}\)[/tex]
c) [tex]\(\{1, 2, 3, 4, 5, 6\}\)[/tex]
d) None of the above
### Option a:
- This set includes the digits 0 through 9 and also includes the '' and '#' symbols.
- A typical phone keypad has the digits 0 to 9 as well as the '' and '#' symbols, making this an inclusive representation.
### Option b:
- This set includes only the digits 0 through 9, which are indeed part of the keypad but it fails to include the '' and '#' symbols.
- Therefore, this set is missing some elements that are present on a typical phone keypad.
### Option c:
- This set includes only the numbers 1 through 6.
- This does not accurately reflect the entirety of a phone keypad, which has 10 digits.
### Option d:
- This option states that none of the above sets represent the sample space correctly.
- Given that option a does represent the keypad fully, this option is not correct.
### Conclusion:
Based on the above breakdown, the sample space that accurately represents the complete set of keys on a typical phone keypad is:
- a) [tex]\(\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , \#\}\)[/tex]
Therefore, the correct answer is:
a) [tex]\(\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , \#\}\)[/tex].
