Question 1182681: Ahmad is fishing in a new pond stocked with 5 catfish, 7 seabass, and 8 tilapia. Ahmad's objective is to catch a Catfish. ifa catfish is not caught. he releases it into the pond and the process is repeated until a catfish is caught. the probability that the second fish caught is seabass is 21/80. find the probability that either the second fish caught is seabass or the forth fish cought is catfish.
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! P((2nd fish is seabass) U (4th fish is catfish)) =
P(2nd fish is seabass) + P(4th fish is catfish) -P((2nd fish is seabass) AND (4th fish is catfish)).
Now P(2nd fish is seabass) = 21/80, while P(4th fish is catfish) =  , since P(fish caught is not catfish) = 3/4 and P(fish caught is catfish) = 1/4.
(Remember the non-catfish caught is thrown back to the pond until a catfish is caught).
==>P(2nd fish is seabass) + P(4th fish is catfish) - P((2nd fish is seabass) AND (4th fish is catfish)) = 21/80 + 27/256 - 1575/32000 =  , or  .
***P((2nd fish is seabass) AND (4th fish is catfish)) = P(s,s,s,c) + P(s,s,t,c)
+ P(t,s,s,c) + P(t,s,t,c) = 1575/32,000.***
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