To find the probability of not selecting a blue marble from the bag, follow these detailed steps:
1. Determine the total number of marbles in the bag:
First, count the number of marbles of each color:
- Blue marbles: 6
- Yellow marbles: 5
- White marbles: 3
- Red marbles: 1
Add these amounts together to find the total number of marbles:
[tex]\[
6 \, \text{(blue)} + 5 \, \text{(yellow)} + 3 \, \text{(white)} + 1 \, \text{(red)} = 15 \, \text{marbles in total}
\][/tex]
2. Determine the number of non-blue marbles:
To find the number of marbles that are not blue, add the numbers of yellow, white, and red marbles:
[tex]\[
5 \, \text{(yellow)} + 3 \, \text{(white)} + 1 \, \text{(red)} = 9 \, \text{non-blue marbles}
\][/tex]
3. Calculate the probability of drawing a non-blue marble:
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Here, the favorable outcomes are the number of non-blue marbles, and the total number of possible outcomes is the total number of marbles in the bag.
[tex]\[
\text{Probability of not selecting a blue marble} = \frac{\text{Number of non-blue marbles}}{\text{Total number of marbles}} = \frac{9}{15}
\][/tex]
4. Simplify the fraction:
To simplify the fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 9 and 15 is 3:
[tex]\[
\frac{9 \div 3}{15 \div 3} = \frac{3}{5}
\][/tex]
So, the probability of not selecting a blue marble is:
[tex]\[
\boxed{\frac{3}{5}}
\][/tex]
Thus, the correct answer is:
A. [tex]\(\frac{3}{5}\)[/tex]
