If the table below represents a probability model based on observed frequencies, what is the value of x

Question

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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

1
1

0.20
0.20

0.10
0.10

0.01

Answer 1

In a probability model, the sum of the probabilities must equal 1. Given the probabilities for the letters Y, C, A, R, and E, you want to find the value of \( x \) for the letter S.

The probabilities provided are:

• \( P(Y) = 0.25 \)
• \( P(C) = 0.18 \)
• \( P(A) = 0.30 \)
• \( P(R) = 0.17 \)
• \( P(E) = x \)
• \( P(S) = 0 \) (since \( x \) is for S)

Now, we can set up the equation:

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

Substituting in the values we have:

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

Now, sum the known probabilities:

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

So now, the equation simplifies to:

\[ 0.90 + x = 1 \]

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

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

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