Question
What is the probability of drawing a prime number from the set {3, 5, 7, 11, 13, 17, 19}?
Answers
GPT-4o mini
To find the probability of drawing a prime number from the set \(\{3, 5, 7, 11, 13, 17, 19\}\), we first identify the total number of elements in the set as well as how many of those elements are prime numbers.
The elements of the set are:
- 3
- 5
- 7
- 11
- 13
- 17
- 19
Each of these elements is a prime number. Therefore, all 7 elements of the set are prime numbers.
Next, we use the formula for probability:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]
In this case, the number of favorable outcomes (drawing a prime number) is 7 (since all elements are prime), and the total number of outcomes (the total number of elements in the set) is also 7.
Thus, the probability is:
\[
\text{Probability} = \frac{7}{7} = 1
\]
Therefore, the probability of drawing a prime number from the set is \(\boxed{1}\).
The elements of the set are:
- 3
- 5
- 7
- 11
- 13
- 17
- 19
Each of these elements is a prime number. Therefore, all 7 elements of the set are prime numbers.
Next, we use the formula for probability:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]
In this case, the number of favorable outcomes (drawing a prime number) is 7 (since all elements are prime), and the total number of outcomes (the total number of elements in the set) is also 7.
Thus, the probability is:
\[
\text{Probability} = \frac{7}{7} = 1
\]
Therefore, the probability of drawing a prime number from the set is \(\boxed{1}\).