Respuesta :
Answer:
Correct option: A
Step-by-step explanation:
The properties of a probability distribution are:
- 0 < P (x = x) < 1.
- ∑ P (X = x) = 1.
The second property implies that the sum of all the probabilities of a random variable is 1.
Use this property to determine the value of x as follows:
[tex]\sum P(X=k)=\frac{5}{12}+\frac{1}{12}+\frac{1}{4}+x[/tex]
[tex]1=\frac{5+1+3+12x}{12}[/tex]
[tex]1=\frac{9+12x}{12}[/tex]
[tex]12=9+12x\\[/tex]
[tex]12x=12-9[/tex]
[tex]12x=3[/tex]
[tex]x=\frac{3}{12}[/tex]
[tex]x=\frac{1}{4}[/tex]
Thus, the missing probability value is [tex]\frac{1}{4}[/tex].
