In a probability distribution, the sum of all probabilities must equal 1.
You have the following probabilities:
- P(3) = 0.4
- P(5) = 0.5
- P(9) = ?
Let \( P(9) = x \). Therefore, we can set up the equation:
\[ 0.4 + 0.5 + x = 1 \]
Combining the known probabilities:
\[ 0.9 + x = 1 \]
To find \( x \), we subtract 0.9 from both sides:
\[ x = 1 - 0.9 \] \[ x = 0.1 \]
Thus, the missing value P(9) is 0.1.