There are 156 fish inside a pond. 50 out of those 156 fish were caught and tagged with a tracking device. What percentage of fish in the pond are now tagged?
2. If 50 of the fish in the pond have been tagged and you catch a fish, what is the probability that it is a tagged fish? If you catch 100 fish how many would you estimate would be tagged fishes?
2007-09-02 15:26:21 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The first one is simply 50/156 = 0.3205
Now the total no. of fish in the pond is too small to be able to use the binomial distribution. This is because we cannot assume p remains constant. Let's do it this way.
There are 50 tagged fish, 106 untagged fish.
He catches 100 fish.
Let's say n of them are tagged and 100-n are untagged.
No. of ways that can happen = N(n)
N(n) = 50Cn * 106C(100-n)
No. of ways of picking 100 fish = 156C100
So P(n) = 50Cn * 106C(100-n) / 156C100
The expected value of n
= E(n) = ∑ n*P(n)
You could tabulate this on an excel spreadsheet, and you'll find that E(n) = 32.05128, rounded to 32. This is the no. of tagged fish you'd expect to get.
Amazingly this value is exactly 50/156 * 100
2007-09-02 18:25:56 · answer #1 · answered by Dr D 7 · 1⤊ 0⤋
1) 50 / 156 fish are tagged which is 0.32051 = 32.051%
2) the prob of catching a tagged fish is 32.051%
if you caught 100 fish you would expect 32 of them to be tagged.
2007-09-04 20:19:18 · answer #2 · answered by Merlyn 7 · 0⤊ 0⤋
50/156=32%
32/100=8/25
32% of 100=32
2007-09-02 22:31:26 · answer #3 · answered by Anonymous · 1⤊ 0⤋
1. about 25%
im not gonna give u an answer for #2. b/c im not 100% sure about my answer so i dont want to give u the wrong answer...i think #1 is what i put.....sorry i could only give you one.
2007-09-02 22:31:35 · answer #4 · answered by Nicole 2 · 1⤊ 0⤋