If ` 10/100, 13/100 , 15/100, 18/100, x/100, 30/100`are the probabilities of 6 observations of an experiment. Find the value of x.

Options

A. 12
B. 13
C. 14
D. 15

Answer

To find the value of \( x \) in the given probabilities \( \frac{10}{100}, \frac{13}{100}, \frac{15}{100}, \frac{18}{100}, \frac{x}{100}, \frac{30}{100} \), we need to use the property that the sum of all probabilities in a probability distribution must equal 1.

### Step-by-Step Solution:

1. **Write down the equation for the sum of probabilities:**
\[ \frac{10}{100} + \frac{13}{100} + \frac{15}{100} + \frac{18}{100} + \frac{x}{100} + \frac{30}{100} = 1 \]

2. **Combine the fractions:**
Since all the probabilities are over a common denominator of 100, we can combine them:
\[ \frac{10 + 13 + 15 + 18 + x + 30}{100} = 1 \]

3. **Calculate the sum of the known probabilities:**
First, we add the known values:
\[ 10 + 13 = 23 \]
\[ 23 + 15 = 38 \]
\[ 38 + 18 = 56 \]
\[ 56 + 30 = 86 \]
So, the equation now looks like:
\[ \frac{86 + x}{100} = 1 \]

4. **Multiply both sides by 100 to eliminate the denominator:**
\[ 86 + x = 100 \]

5. **Solve for \( x \):**
Subtract 86 from both sides:
\[ x = 100 - 86 \]
\[ x = 14 \]

### Final Answer:
The value of \( x \) is \( 14 \).

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