Question

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

0.01
0.01

1
1

0.10

Answer 1

To determine the value of \( x \) in the probability model, we need to use the fact that the probabilities should sum to 1. The given probabilities are:

- \( P(Y) = 0.25 \)
- \( P(C) = 0.18 \)
- \( P(A) = 0.30 \)
- \( P(R) = 0.17 \)
- \( P(E) = x \)
- \( P(S) = 1 - (0.25 + 0.18 + 0.30 + 0.17 + x) \) (but we only need the sum of the given probabilities)

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

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

Since the total probability must equal 1, we can set up the equation:

\[
0.90 + x = 1
\]

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

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

Thus, the value of \( x \) is **0.10**.