a bag contains twelve balls labeled 1 through 12. one ball will be randomly picked. what is the probability…

a bag contains twelve balls labeled 1 through 12. 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.

a bag contains twelve balls labeled 1 through 12. 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.

Answer

Explanation:

Step1: Determine total number of outcomes

There are 12 balls, so total number of outcomes ( n(S)=12 ).

Step2: Find number of favorable outcomes

Multiples of 3 from 1 - 12 are 3, 6, 9, 12. So number of favorable outcomes ( n(A) = 4 ).

Step3: Calculate probability

Probability formula is ( P(A)=\frac{n(A)}{n(S)} ). Substituting values, ( P(A)=\frac{4}{12} ). Simplify the fraction: ( \frac{4\div4}{12\div4}=\frac{1}{3} ).

Answer:

(\frac{1}{3})