Question

a bag contains seven balls labeled 1 through 7. one ball will be randomly picked. what is the probability of picking an even number? write your answer as a fraction in simplest form.

Explanation:

Step1: Determine total number of outcomes

There are 7 balls (labeled 1 - 7), so total number of possible outcomes \( n(S)=7 \).

Step2: Determine number of favorable outcomes

Even - numbered balls are 2, 4, 6. So number of favorable outcomes \( n(E) = 3 \).

Step3: Use probability formula

Probability formula is \( P(E)=\frac{n(E)}{n(S)} \). Substituting values, \( P(E)=\frac{3}{7} \).

Answer:

\(\frac{3}{7}\)