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

0.20
0.20

1
1

0.10
0.10

0.01
0.01
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Answer 1

In a probability model, the sum of the probabilities must equal 1.

We can set up the equation based on the given probabilities:

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

Substituting the known values from the table:

\[
0.25 + 0.18 + 0.30 + 0.17 + x + P(S) = 1
\]

Now, first, let's add the known probabilities:

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

So the equation becomes:

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

This implies:

\[
x + P(S) = 1 - 0.90
\]
\[
x + P(S) = 0.10
\]

If we assume that P(S) refers to the same x value, we can deduce that:

\[
x = 0.10
\]

If we were not assuming P(S) = 0, and given the options provided, we can separately calculate it:

From the possible values `0.20`, `0.10`, and `0.01`, the fraction that fits our equation would be

So the solution with x being `0.10` is valid based on the sum constraints.

Thus, the value of x is **0.10**.