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

0.01
0.01

0.20
0.20

1
1

0.10

Answer 1

In a probability model, the sum of all probabilities must equal 1. Given the probabilities for Y, C, A, R, and S, we have:

• P(Y) = 0.25
• P(C) = 0.18
• P(A) = 0.30
• P(R) = 0.17
• P(E) = x

We can set up the equation based on the fact that the total probability must equal 1:

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

Substituting in the values we have:

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

Calculating the sum of known probabilities:

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

Now substitute this back into the equation:

\[ 0.90 + x = 1 \]

To solve for x, subtract 0.90 from both sides:

\[ x = 1 - 0.90 \]

\[ x = 0.10 \]

The value of \( x \) is 0.10.