A bag contains 5 red​ marbles, 3 blue​ marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the​ bag?

Answer 1

To find the probability of choosing a marble that is not blue, we first need to determine the total number of marbles in the bag and then the number of marbles that are not blue.

1. Total number of marbles:

   • Red marbles: 5
   • Blue marbles: 3
   • Green marbles: 1

   Total = 5 + 3 + 1 = 9 marbles

2. Number of marbles that are not blue:

   • Red marbles: 5
   • Green marbles: 1

   Total non-blue marbles = 5 + 1 = 6 marbles

3. Probability of choosing a non-blue marble: The probability \( P \) of choosing a non-blue marble is given by the ratio of the number of non-blue marbles to the total number of marbles:

   \[ P(\text{not blue}) = \frac{\text{Number of non-blue marbles}}{\text{Total number of marbles}} = \frac{6}{9} \]

4. Simplifying the fraction: \[ P(\text{not blue}) = \frac{6}{9} = \frac{2}{3} \]

Therefore, the probability of choosing a marble that is not blue is \(\frac{2}{3}\).