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

0.10
0.10

1
1

0.01
0.01
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Answer 1

In a probability model, the sum of all the probabilities must equal 1. From the table provided, we have the following probabilities:

- P(Y) = 0.25
- P(C) = 0.18
- P(A) = 0.30
- P(R) = 0.17
- P(E) = x
- P(S) is not given, but we can assume it follows the same pattern as the others.

To solve for x, we can sum the known probabilities and set the equation as follows:

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

Given that the probabilities of Y, C, A, and R are:

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

Calculating the known sums:

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

Now, our equation simplifies to:

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

Now, we need to find the value of \( x \) and make an assumption about \( P(S) \). If we assume \( P(S) = 0 \) (or simply that \( S \) is not happening), we can solve for \( x \):

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

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