At Fontaine Lake Camp on Lake Athabasca in northern Canada, history shows that a

Question

At Fontaine Lake Camp on Lake Athabasca in northern Canada, history shows that about 25% 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. (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 fishing trips that must be taken to catch the first lake trout over 20 pounds?

Explanation / Answer

this is a geomteric distribution

a)P(n) =(0.75)n-1*0.25

b)from above formual probability P(n=3) =(0.75)2*0.25 =0.141

c)probabilty P(n>3) = no success in first 3 attempts =(0.75)3 =0.422

d)expected numbr =1/p =1/0.25 =4

  

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