PROBABILITY DENSITY FUNCTIONS!! HELP WITH ONE PART!!!!

Question

Assume that the machine yields the item selected 75 percent of the time, and returns nothing 25 percent of the time. Three individuals attempt to use the machine. Let X be defined as the number of individuals who obtain the item selected.

How many different values are possible for the random variable X? ANSWER IS 4

Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order.

THIS IS THE PART I NEED HELP WITH (I DON'T UNDERSTAND HOW TO GET PROBABILITY)

X     PROBABILITY

0     ___________

1     ___________

2     ___________

3     ___________

Answer 1

 

Hi Mauro,

 

X = i, i = 0, 1, 2, 3, means i people out of 3 obtained the item selected.

 

X = 0 means nobody got the item selected, so

 

     Prob(X = 0) = ₃C₀ · 0.25 · 0.25 · 0.25

 

                       = 1/64

 

                       = 0.0156

 

X = 1 means only one person got the item selected, so

 

     Prob(X = 1) = ₃C₁ · 0.75 · 0.25 · 0.25

 

                       = 3 · 0.75 · 0.25 · 0.25

 

                       = 9/64

 

                       = 0.1406

 

X = 2 means only two people got the item selected, so

 

     Prob(X = 2) = ₃C₂ · 0.75 · 0.75 · 0.25
 
                       = 3 · 0.75 · 0.75 · 0.25

 

                       = 27/64

 

                       = 0.4219

 

X = 3 means all three people got the item selected, so
 
     Prob(X = 3) = ₃C₃ · 0.75 · 0.75 · 0.75

                       = 27/64

 

                       = 0.4219