Chapter 6.3, Problem 25P

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 fishing 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 lakes more than three trips for a guest to catch a lake trout weighing at least 20 pounds.

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

Hint: See Problem 23.