To determine the probability that a randomly selected marble from the bag is neither white nor blue, we will follow these steps:
1. Calculate the total number of marbles in the bag:
The table provides the number of marbles of each color. Let's sum these to find the total number of marbles:
[tex]\[
26 + 25 + 25 + 13 + 26 = 115
\][/tex]
So, the total number of marbles in the bag is 115.
2. Calculate the number of marbles that are not white or blue:
We add the number of marbles that are red, green, and pink since these are the colors we're interested in:
[tex]\[
26 \text{ (red)} + 25 \text{ (green)} + 13 \text{ (pink)} = 64
\][/tex]
So, there are 64 marbles that are not white or blue.
3. Express the probability as a fraction:
The probability [tex]\( P \)[/tex] of picking a marble that is not white or blue is the ratio of the number of favorable outcomes (marbles that are red, green, or pink) to the total number of outcomes (total marbles):
[tex]\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{64}{115}
\][/tex]
The fraction [tex]\(\frac{64}{115}\)[/tex] is already in its lowest terms since 64 and 115 have no common divisors other than 1.
4. Convert the fraction to a decimal:
We divide 64 by 115 to find the decimal representation of this probability:
[tex]\[
\frac{64}{115} \approx 0.556522
\][/tex]
When rounded to the nearest millionth (six decimal places), the decimal form is:
[tex]\[
0.556522
\][/tex]
Therefore, the probability that a randomly selected marble is a color other than white or blue is:
- Fraction: [tex]\(\frac{64}{115}\)[/tex]
- Decimal: [tex]\(0.556522\)[/tex]
This completes the solution.
