Question

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

0.20
0.20

0.10
0.10

1

Answer 1

To determine the value of \( x \) in the probability model, we need to remember that the sum of the probabilities must equal 1.

The given probabilities are:
- \( P(Y) = 0.25 \)
- \( P(C) = 0.18 \)
- \( P(A) = 0.30 \)
- \( P(R) = 0.17 \)
- \( P(E) = x \)

Setting up the equation:

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

Substituting in the known values:

\[
0.25 + 0.18 + 0.30 + 0.17 + x = 1
\]

Calculating the sum of the known probabilities:

\[
0.25 + 0.18 = 0.43
\]
\[
0.43 + 0.30 = 0.73
\]
\[
0.73 + 0.17 = 0.90
\]

Now substitute back into the equation:

\[
0.90 + x = 1
\]

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

\[
x = 1 - 0.90 = 0.10
\]

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

So the correct response is:

**0.10**