A consumer looking to buy a used red Miata car will call dealerships until she finds a dealership that carries the car. She estimates the probability that any independent dealership will have the car will be $28 %$ . We are interested in the number of dealerships she must call.
a. In words, define the random variable $X$ .
b. List the values that X may take on.
c. Give the distribution of $X$ . $X$ ~ ___(_,___)
d. On average, how many dealerships would we expect her to have to call until she finds one that has the car?
e. Find the probability that she must call at most four dealerships.
f. Find the probability that she must call three or four dealerships

Question

Accepted Answer

a. The variable quantity $X$ is the quantity of dealership the customer must call before she finds a second user red Miata car.

b. The values of X are $X = 1, 2, 3, 4, . . . .$

c. The distribution of X is $X ~ G (0.28)$

d. The expected number of dealership she would have to find is $3.57$

e. The probability that she must out in most four dealerships $0.7313$

f. The probability that she must call three or four dealerships $0.2497$

Short Answer