Question

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

0.01
0.01

0.10
0.10

1
1

0.20

Answer 1

In a probability model, the sum of the probabilities must equal 1. This means we can set up the equation:

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

Substituting the given probabilities into the equation:

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

Since \( P(S) \) is not given, we will assume it is part of the table and allows us to find \( x \).

Now we will first calculate the sum of the known probabilities:

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

Now we can write the equation as:

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

From the equation, it follows that:

\[
x + P(S) = 1 - 0.90
\]
\[
x + P(S) = 0.10
\]

If we denote \( P(S) \) as \( x \) (assuming for this particular problem that is the variable we seek), the simplified equation becomes:

\[
x + x = 0.10
\]
\[
2x = 0.10
\]
\[
x = 0.05
\]

However, since that value does not appear in the answer choices, we can deduce that the observable options only have x.

Thus, we can reason \( P(S) \) shall be looked at, and check all available responses:

Given \( P(S) + x = 0.10 \) implies only \( x \) should balance here, thus we ascertain by closeness that it must be \( 0.10 \) as stated.

Therefore, the value of \( x \) that fits the probability model is 0.10.

So, the answer is:

**0.10**