There are 50 marbles of 3 colours: blue, yellow and black. The probability of picking up a blue marble is 3/10 and that of picking up a yellow marble is 1/2. The probability of picking up a black marble is

Options

A. `1//5`
B. `1//10`
C. `1//4`
D. `4//5`

Answer

To find the probability of picking a black marble from a total of 50 marbles of three colors (blue, yellow, and black), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the total number of marbles:**
- Total marbles = 50

2. **Identify the probabilities given:**
- Probability of picking a blue marble (P(Blue)) = 3/10
- Probability of picking a yellow marble (P(Yellow)) = 1/2

3. **Calculate the number of blue marbles:**
- The probability of blue marbles can be expressed as:
\[ P(Blue) = \frac{\text{Number of Blue Marbles}}{\text{Total Number of Marbles}} \]
- Let the number of blue marbles be \( x \):
\[ \frac{x}{50} = \frac{3}{10} \]
- Cross-multiplying gives:
\[ 10x = 3 \times 50 \]
\[ 10x = 150 \]
\[ x = \frac{150}{10} = 15 \]
- So, there are 15 blue marbles.

4. **Calculate the number of yellow marbles:**
- Similarly, for yellow marbles:
\[ P(Yellow) = \frac{\text{Number of Yellow Marbles}}{\text{Total Number of Marbles}} \]
- Let the number of yellow marbles be \( y \):
\[ \frac{y}{50} = \frac{1}{2} \]
- Cross-multiplying gives:
\[ 2y = 1 \times 50 \]
\[ 2y = 50 \]
\[ y = \frac{50}{2} = 25 \]
- So, there are 25 yellow marbles.

5. **Calculate the number of black marbles:**
- The total number of marbles is the sum of blue, yellow, and black marbles:
\[ \text{Total} = \text{Blue} + \text{Yellow} + \text{Black} \]
- We already found:
\[ 50 = 15 + 25 + \text{Black} \]
- Rearranging gives:
\[ \text{Black} = 50 - 15 - 25 \]
\[ \text{Black} = 10 \]
- So, there are 10 black marbles.

6. **Calculate the probability of picking a black marble:**
- The probability of picking a black marble (P(Black)) is given by:
\[ P(Black) = \frac{\text{Number of Black Marbles}}{\text{Total Number of Marbles}} = \frac{10}{50} \]
- Simplifying gives:
\[ P(Black) = \frac{1}{5} \]

### Final Answer:
The probability of picking up a black marble is \( \frac{1}{5} \).