To find the value of \( x \) in the probability model, we need to remember that the sum of all probabilities must equal 1.
From your table, we have the probabilities:
- \( P(Y) = 0.25 \)
- \( P(C) = 0.18 \)
- \( P(A) = 0.30 \)
- \( P(R) = 0.17 \)
- \( P(E) = x \)
- \( P(S) = 1 - (0.25 + 0.18 + 0.30 + 0.17 + x) \)
We can set up the equation as follows:
\[ 0.25 + 0.18 + 0.30 + 0.17 + x + P(S) = 1 \]
First, we calculate the sum of the known probabilities:
\[ 0.25 + 0.18 + 0.30 + 0.17 = 0.90 \]
This means:
\[ 0.90 + x + P(S) = 1 \]
If we denote \( P(S) \) as \( 1 - (0.90 + x) \):
\[ P(S) = 1 - 0.90 - x \]
Since \( P(S) \) should also be a probability, it must be non-negative. Let's then write \( P(S) = 0.10 - x \) such that \(0.10 - x = 0\) and set the limits:
This means that:
\[ 0.10 \geq x \geq 0 \]
So, the only possible non-negative values of \( x \) that fit the probability model must be equal to:
\[ x = 0.10 \]
In the options provided, the value of \( x \) is therefore:
0.10.