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Question

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

Solution

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1 of 2Given:

$p=30\%=0.30$

A variable of a binomial experiment that measures the amount of trials needed until the first success uses the geometric distribution.

The mean of the geometric distribution is the reciprocal of $p$:

$\mu=\dfrac{1}{p}=\dfrac{1}{0.30}\approx 3.3333\approx 3$

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