In the year 2019, the proportion of U.S. major league baseball players who were foreign born was 251 out of 882. Suppose we begin to randomly select major league players until we find one who is foreign born. Such an experiment can be described by the geometric distribution, for which the probability of success after x tries is given by

where p is the probability of success on a given try.

(a) Verify that ƒ describes a probability distribution by showing that

(b) Calculate the expected value for ƒ, given by

(c) On average, how many major league baseball players would you expect to meet before meeting one who is foreign born?
(d) What is the probability that you meet a foreign-born player within the first three major league players that you meet?

Transcribed Image Text:

f(x) = (1 − p)*-¹p, x = 1, 2, 3, ...