In a probability model, the sum of all the probabilities must equal 1. From the table provided, we have the following probabilities:
- P(Y) = 0.25
- P(C) = 0.18
- P(A) = 0.30
- P(R) = 0.17
- P(E) = x
- P(S) is not given, but we can assume it follows the same pattern as the others.
To solve for x, we can sum the known probabilities and set the equation as follows:
\[ P(Y) + P(C) + P(A) + P(R) + P(E) + P(S) = 1 \]
Given that the probabilities of Y, C, A, and R are:
\[ 0.25 + 0.18 + 0.30 + 0.17 + x + P(S) = 1 \]
Calculating the known sums:
\[ 0.25 + 0.18 + 0.30 + 0.17 = 0.90 \]
Now, our equation simplifies to:
\[ 0.90 + x + P(S) = 1 \]
Now, we need to find the value of \( x \) and make an assumption about \( P(S) \). If we assume \( P(S) = 0 \) (or simply that \( S \) is not happening), we can solve for \( x \):
\[ 0.90 + x = 1 \] \[ x = 1 - 0.90 = 0.10 \]
Thus, the value of \( x \) is 0.10.