If da table below represents a probability model based on observed frequencies, wut is da value of x?

Question

Dis table shows a probability model for da letter Y, C, A, R, E, and S based on observed frequiences

Y P (Y)

C 0.25

A 0.18

R 0.30

E 0.17

S x

A ) 1

B ) 0.10

C ) 0.01

D ) 0.20

Answer 1

In a probability model, the sum of all probabilities must equal 1. You have the probabilities for the letters C, A, R, and E, and you need to find the probability for S, represented as \( x \).

Let's calculate the sum of the known probabilities:

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

Calculating this sum:

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

Now, since the total probability must equal 1, we have:

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

This means:

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

So, the value of \( x \) (i.e., \( P(S) \)) is \( 0.10 \).

The answer is:

B) 0.10.