Answer:
The probability that the first subject to be a universal blood donor is the seventh person selected is 0.0511
Step-by-step explanation:
Let's start defining the random variable X.
X : ''The first success is on the xth trial''
X can be modeled as a geometric random variable with the following probability function :
[tex]P(X=x)=p(1-p)^{x-1}[/tex]
Where [tex]P(X=x)[/tex] is the probability of the random variable X to assumes the value ''x''.
The variable p is the success probability.
For this exercise, we define a success as someone randomly selected is a universal donor and that probability is [tex]p=0.09[/tex]
We are looking for : [tex]P(X=7)[/tex]
The probability function is :
[tex]P(X=x)=(0.09)(0.91)^{x-1}[/tex]
[tex]P(X=7)=(0.09)(0.91)^{7-1}=(0.09)(0.91)^{6}=0.0511[/tex]
