Question

a bag contains eleven balls labeled 1 through 11. one ball will be randomly picked. what is the probability of picking a multiple of 3? write your answer as a fraction in simplest form.

Explanation:

Step1: Determine total number of balls

There are 11 balls labeled 1 through 11. So, total number of possible outcomes \( n(S)=11 \).

Step2: Find number of favorable outcomes

Multiples of 3 between 1 and 11 are 3, 6, 9. So, number of favorable outcomes \( n(A) = 3 \).

Step3: Calculate probability

Probability formula is \( P(A)=\frac{n(A)}{n(S)} \). Substituting values, \( P(A)=\frac{3}{11} \).

Answer:

\(\frac{3}{11}\)