Question

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.

Answer 1

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 :

$P(X=x)=p(1-p)^{x-1}$

Where $P(X=x)$ 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 $p=0.09$

We are looking for : $P(X=7)$

The probability function is :

$P(X=x)=(0.09)(0.91)^{x-1}$

$P(X=7)=(0.09)(0.91)^{7-1}=(0.09)(0.91)^{6}=0.0511$