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 0.01 0.01 1 1 0.20 0.20 0.10 0.10 Skip to navigation

Answer 1

To find the value of \( x \), we first need to recall that the sum of all probabilities in a probability model must equal 1. The given probabilities are:

- \( P(Y) = 0.25 \)
- \( P(C) = 0.18 \)
- \( P(A) = 0.30 \)
- \( P(R) = 0.17 \)
- \( P(E) = x \)
- \( P(S) = 1 - (0.25 + 0.18 + 0.30 + 0.17 + x) \)

Summing the known probabilities, we get:

\[
P(Y) + P(C) + P(A) + P(R) = 0.25 + 0.18 + 0.30 + 0.17 = 0.90
\]

Now we can set up the equation for \( x \):

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

Since the sum of all probabilities must equal 1, we have:

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

This means:

\[
0.90 + x + (1 - (0.90 + x)) = 1
\]

Solving for \( x \):

Since we have established no other values for \( P(S) \), assuming typical settings, we should have \( P(S) = 0 \) (meaning \( x \) must adjust to ensure \( P(S) + 0.90 + x = 1\)).

Thus if:

\[
x = 1 - 0.90 = 0.10
\]

Now let's check:

When \( x = 0.10 \), it gives us \( P(S) = 1 - 0.90 - 0.10 = 0.00 \).

This meets the condition of summation, making this a valid probability model.

Thus, the solution confirms the value of \( x \) as:

\[
\boxed{0.10}
\]