Question
The table below shows an incomplete probability density function for the number of errors, $X$, found in a machine during a monthly quality control inspection at a textile factory. What should the missing probability be?
- Provide the final answer as a fraction.
\begin{tabular}{|c|c|}
\hline$x$ & $P(X=x)$ \\
\hline 0 & $1 / 2$ \\
\hline 1 & $1 / 3$ \\
\hline 2 & \\
\hline
\end{tabular}
Provide your answer below:
Answer
Final Answer: The missing probability should be \(\boxed{\frac{1}{6}}\).
Step 1 ：The sum of all probabilities in a probability density function must equal 1. Therefore, to find the missing probability, we need to subtract the sum of the given probabilities from 1.
Step 2 ：Given that the probability of 0 errors is \(\frac{1}{2}\) and the probability of 1 error is \(\frac{1}{3}\), we can calculate the missing probability as follows:
Step 3 ：\(1 - \frac{1}{2} - \frac{1}{3} = \frac{1}{6}\)
Step 4 ：Final Answer: The missing probability should be \(\boxed{\frac{1}{6}}\).
