A fishing lake camp boasts that about 30% of the guests catchlake trout over 20 pounds on a 4-day fishing trip. Let nbe a random variable that represents the first trip to thecamp on which a guest catches a lake trout over 20 pounds.
(a) Write out a formula for the probability distribution of therandom variable n.
P(n) =
(b) Find the probability that a guest catches a lake trout weighingat least 20 pounds for the first time on trip number 3.(Round your answer to three decimal places.)
(c) Find the probability that it takes more than three trips for aguest to catch a lake trout weighing at least 20 pounds. (Roundyour answer to three decimal places.)
(d) What is the expected number of fishing trips that must be takento catch the first lake trout over 20 pounds? Hint: Useμ for the geometric distribution and round. (Round youranswer to two decimal places.)
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