a)

Pr[x>=a]<=(E[x]/a)   <- def of markov inqeuality
Let x be number of hours to catch a fish
plug in numbers: E[x]=1 (given)   a=3b (given)
so we get:
Pr[take 3 hours to catch a fish]= Pr[x>=3]<=(1/3)

b)

Pr[not catch any fish in 2 hours]
= 1 - Pr[catch fish in 2+ hours] 
= 1 - (Pr[x>=2]<=(1/2))
>=(1/2)

Alumni Liaison

Prof. Math. Ohio State and Associate Dean
Outstanding Alumnus Purdue Math 2008

Jeff McNeal