If a procedure meets all of the conditions of a binomial distribution except the number of trials is not fixed, then the geometric distribution can be used. the probability of getting the first success on the xth trial is given by p(x)equalsp (1 minus p )superscript x minus 1, where p is the probability of success on any one trial. subjects are randomly selected for a health survey. the probability that someone is a universal donor (with group o and type rh negative blood) is 0.09. find the probability that the first subject to be a universal blood donor is the seventh person selected.

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 :

Where 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

We are looking for :

The probability function is :