Question

Assume that
the fisherman can use between 3 and 6 lines. With 3 lines, the probability
of a catch on each line is 0.77. With 4 this probability is 0.62, with
5 it is 0.51, and with 6 the probability is 0.42.


How many lines should the fisherman use to maximize the probability of catching
at least 2 fish?

Answer 1

its not 4 or 5

Answer 2

i got same, answer was 5 and it said it was incorrect.

Answer 3

i got answer 3 with Pr=.4091

Answer 4

is that right?

Answer 5

Remember, in probability, each line will be treated as an individual event. The values calculated by @Calcmathlete are incorrect as the probability exceeds 1. Remember, for any given event the probability can NEVER be greater than 1 or less than 0.

In all these scenarios, he has to catch AT LEAST 2 fish so there can be 2 or more fish in each case.

So lets look at it case by case:

with 3 lines:
P (at least 2 fish) = P(3 fishes) or P(2 fishes)
P (at least 2 fish) = (0.77^3) + [(0.77^2) * 0.23]
P (at least 2 fish) = 0.5929

with 4 lines:
P (at least 2 fish) = P(4 fishes) or P(3 fishes) or P(2 fishes)
P (at least 2 fish) = (0.62^4) + [(0.62^3) * 0.38] + [0.62^2 + 0.38^2]
P (at least 2 fish) = 0.2938

with 4 lines:
P (at least 2 fish) = P(5 fishes) or P(4 fishes) or P(3 fishes) or P(2 fishes)
P (at least 2 fish) = (0.51^5) + [(0.51^4) * 0.49)] + [(0.51^3) * (0.49^2)] + [0.51^2 + 0.49^3]
P (at least 2 fish) = 0.1301

It is obvious from here that with 6 lines, this probability will decrease. So you use 3 lines. The probability will be 0.5929

Answer 6

Oh. Sorry. I didn't know that.

Answer 7

mubzz I sooo appreciate your help. I like Baye's Probability better haha it's easier to figure out

Answer 8

Haha yea there are definitely several ways to approach any given problem. As long as you stick to the principles, no restriction on what method you use :D Good luck!

Answer 9

Thank You!