Expand Your Knowledge: Geometric Distribution; Fishing At Fontaine Lake Camp on Lake Athabasca in northern Canada, history shows that about 30%

of the guests catch lake trout over 20 pounds on a 4-day fi shing trip (Source:

Athabasca Fishing Lodges, Saskatoon, Canada). Let n be a random variable that represents the first trip to Fontaine Lake Camp on which a guest catches a lake trout over 20 pounds.

(a) Write out a formula for the probability distribution of the random variable n.

(b) Find the probability that a guest catches a lake trout weighing at least 20 pounds for the first time on trip number 3.

(c) Find the probability that it takes more than three trips for a guest to catch a lake trout weighing at least 20 pounds.

(d) What is the expected number of fi shing trips that must be taken to catch the fi rst lake trout over 20 pounds? Hint: Use m for the geometric distribution and round.

Hint: See Problem 23.