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

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

1
1

0.01
0.01

0.10
0.10

0.20

:)

1 answer

To find the value of \( x \) in the probability model, we need to remember that the sum of probabilities in a probability model must equal 1. We can set up the equation based on the given probabilities:

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

Substituting the values we have:

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

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

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

Now, we place our sum back into the equation:

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

Assuming \( P(S) \) represents the probability of \( P(E) \) (which seems to be the missing value), the sum simplifies to:

\[ 0.90 + x = 1 \]

Thus, we can solve for \( x \):

\[ x = 1 - 0.90 = 0.10 \]

This value represents the unseen probability for letter \( E \). Therefore, the value of \( x \) is:

\[ \boxed{0.10} \]