A bag contains red, white and blue marbles. The probability of selecting a red marble is `(2)/(15)` and that of selecting a blue marble is `(4)/(15)` . The probability of selecting a white marble is

Options

A. `(13)/(15)`
B. `(11)/(15)`
C. `(3)/(5)`
D. `(2)/(5)`

Answer

To find the probability of selecting a white marble from the bag, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Total Probability**: The total probability of all outcomes in a probability scenario must equal 1. Therefore, we can write the equation:
\[ P(\text{Red}) + P(\text{White}) + P(\text{Blue}) = 1 \]

2. **Substitute Known Probabilities**: We know the probabilities of selecting a red and a blue marble:
\[ P(\text{Red}) = \frac{2}{15}, \quad P(\text{Blue}) = \frac{4}{15} \]
Substitute these values into the equation:
\[ \frac{2}{15} + P(\text{White}) + \frac{4}{15} = 1 \]

3. **Combine the Known Probabilities**: Add the probabilities of the red and blue marbles:
\[ \frac{2}{15} + \frac{4}{15} = \frac{6}{15} \]

4. **Set Up the Equation for White Marble Probability**: Now, we can substitute this back into the equation:
\[ \frac{6}{15} + P(\text{White}) = 1 \]

5. **Isolate the Probability of White Marble**: To find \( P(\text{White}) \), subtract \( \frac{6}{15} \) from 1:
\[ P(\text{White}) = 1 - \frac{6}{15} \]

6. **Convert 1 to a Fraction with a Common Denominator**: Convert 1 into a fraction with a denominator of 15:
\[ 1 = \frac{15}{15} \]

7. **Perform the Subtraction**: Now, subtract the fractions:
\[ P(\text{White}) = \frac{15}{15} - \frac{6}{15} = \frac{9}{15} \]

8. **Simplify the Fraction**: Finally, simplify \( \frac{9}{15} \):
\[ P(\text{White}) = \frac{3}{5} \]

### Final Answer:
The probability of selecting a white marble is \( \frac{3}{5} \).

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