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

0.20
0.20

0.10
0.10

0.01
0.01

1

Answer 1

To find the value of \( x \), we need to ensure that the total probability sums to 1, as per the rules of probability.

Taking the probabilities provided in the table:

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

Substituting the values into the equation:

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

Now, we can sum the known probabilities:

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

Now we have:

\[ 0.90 + x = 1 \]

To solve for \( x \):

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

So the value of \( x \) is 0.10.