Question

a bag with 12 marbles has 3 blue marbles, 4 yellow marbles, and 5 red marbles. a marble is chosen from the bag at random. what is the probability that it is not blue? write your answer as a fraction in simplest form.

Explanation:

Step1: Calculate the number of non - blue marbles

The number of non - blue marbles is the sum of yellow and red marbles. So, \(4 + 5=9\).

Step2: Use the probability formula

The probability formula is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (non - blue marbles) is \(9\) and the total number of outcomes (total marbles) is \(12\). So the probability is \(\frac{9}{12}\).

Step3: Simplify the fraction

Simplify \(\frac{9}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(3\). \(\frac{9\div3}{12\div3}=\frac{3}{4}\).

Answer:

\(\frac{3}{4}\)