If the table below represents a probability model based on observed frequencies, what is the value of x ? This table shows a probability model for the letters Y, C, A, R, E, and S based on observed frequencies. Y C A R E S P(Y) 0.25 0.18 0.30 0.17 x (1 point) Responses 0.20 0.20 0.10 0.10 1 1 0.01

Answer 1

In a probability model, the sum of all probabilities must equal 1. Given the probabilities for the letters Y, C, A, R, and E, we can find the value of \( x \) by setting up the following equation:

\[ P(Y) + P(C) + P(A) + P(R) + P(E) + P(S) = 1 \]

Substituting the values we have:

\[ 0.25 + 0.18 + 0.30 + 0.17 + x = 1 \]

Now, let's calculate the sum of the known probabilities:

\[ 0.25 + 0.18 + 0.30 + 0.17 = 0.90 \]

Now we can plug this back into the equation:

\[ 0.90 + x = 1 \]

To find \( x \), we subtract 0.90 from both sides:

\[ x = 1 - 0.90 = 0.10 \]

Therefore, the value of \( x \) is:

\[ \boxed{0.10} \]