If the table below represents a probability model based on observed frequencies, what is the value of x

Question

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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

1
1

0.01
0.01

0.10

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 the value of \( x \) for E, we can set up the following equation to find \( x \):

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

Substituting the given probabilities into the equation:

\[ 0.25 + 0.18 + 0.30 + 0.17 + x + P(S) = 1 \]

Now, let's sum the known probabilities:

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

Now we can substitute this into our equation:

\[ 0.90 + x + P(S) = 1 \]

Assuming P(S) is not given (since we haven't any value for it), we will just consider:

\[ 0.90 + x = 1 \]

Solving for \( x \):

\[ x = 1 - 0.90 \] \[ x = 0.10 \]

Therefore, the value of \( x \) is 0.10.