If the table below represents a probability model based on observed frequencies, what is the value of x?
C A R E S
P(Y) 0.25 0.18 0.30 0.17 x
Responses
0.20
0.20
1
1
0.01
0.01
0.10
0.10.
To find the value of x, we can use the fact that the sum of all the probabilities in a probability model must equal 1.
0.25 + 0.18 + 0.30 + 0.17 + x = 1
Simplifying, we get:
x = 1 - (0.25 + 0.18 + 0.30 + 0.17)
x = 1 - 0.90
x = 0.10
To find the value of x, we need to sum up all the probabilities in the P(Y) column and subtract the result from 1 since the sum of all probabilities should equal 1.
Sum of probabilities in the P(Y) column = 0.25 + 0.18 + 0.30 + 0.17 + x
Since the sum of probabilities should equal 1, we can write the equation:
0.25 + 0.18 + 0.30 + 0.17 + x = 1
Simplifying the equation, we have:
0.90 + x = 1
Subtracting 0.90 from both sides, we get:
x = 1 - 0.90
x = 0.10
Therefore, the value of x is 0.10.