To find the probability of picking an even number from the list, we follow these steps:
Step 1: List all even numbers in the set.
Step 2: Count how many even numbers there are.
Step 3: Count the total number of numbers in the set.
Step 4: Divide the number of even numbers by the total number of numbers to find the probability.
Now, let's work through these steps with the given list:
\[ \text{Set} = \{2, 4, 5, 7, 9, 10, 12, 15, 18, 20\} \]
Step 1: Identify the even numbers.
Even numbers in the list are: 2, 4, 10, 12, 18, 20
Step 2: Count the even numbers.
There are 6 even numbers.
Step 3: Count the total number of numbers in the list.
There are 10 numbers in total.
Step 4: Calculate the probability of selecting an even number.
The probability \( P \) of picking an even number is the ratio of the number of even numbers to the total number of numbers:
\[ P(\text{even number}) = \frac{\text{Number of even numbers}}{\text{Total number of numbers}} \]
\[ P(\text{even number}) = \frac{6}{10} \]
To express the probability in the simplest form of a fraction, we reduce the fraction by dividing the numerator and the denominator by their greatest common divisor which is 2:
\[ P(\text{even number}) = \frac{6 \div 2}{10 \div 2} \]
\[ P(\text{even number}) = \frac{3}{5} \]
So, the probability of randomly picking an even number from the list in the simplest form of a fraction is \( \frac{3}{5} \).
