To find the probability of drawing a card that is either a composite numbered card or a prime numbered card from a group of cards numbered from 2 to 16, we need to follow these steps:
1. Identify the Range of Cards: The cards are numbered from 2 to 16. Therefore, the total number of cards is:
[tex]\[
\text{Total number of cards} = 16 - 2 + 1 = 15
\][/tex]
2. Identify Composite Numbers and Prime Numbers:
- A composite number is a positive integer that has at least one positive divisor other than one or itself.
- A prime number is a positive integer greater than 1 that has no positive divisors other than one and itself.
- Here are the composite numbers within the range 2 to 16:
[tex]\[
4, 6, 8, 9, 10, 12, 14, 15, 16
\][/tex]
- Here are the prime numbers within the range 2 to 16:
[tex]\[
2, 3, 5, 7, 11, 13
\][/tex]
3. Count the Composite Numbers:
- The number of composite cards is 9.
4. Count the Prime Numbers:
- The number of prime cards is 6.
5. Total Composite or Prime Cards:
- Since there are no other types of numbers (2-16 are either composite or prime), the count of composite or prime cards is:
[tex]\[
9 + 6 = 15
\][/tex]
6. Calculate the Probability:
- The probability [tex]\(P(\text{composite or prime card})\)[/tex] is the number of favorable outcomes (composite or prime cards) divided by the total number of possible outcomes (total cards):
[tex]\[
P(\text{composite or prime card}) = \frac{\text{Number of composite or prime cards}}{\text{Total number of cards}} = \frac{15}{15} = 1.0
\][/tex]
Therefore, the probability of drawing a card that is either a composite numbered card or a prime numbered card is:
[tex]\[
\boxed{1.0}
\][/tex]
