Question

a pond is freshly stocked with 6 brown trout and 18 lake trout. the first fisherman in the area catches and releases a trout. he catches another trout a while later.
what is the probability that the fisherman caught brown trout each time?
1/8
1/16
5/32
5/16

Explanation:

Step1: Calculate the total number of trouts

The total number of trouts is \(6 + 18=24\).

Step2: Calculate the probability of catching a brown trout the first time

The probability of catching a brown trout the first time is \(\frac{6}{24}=\frac{1}{4}\).

Step3: Calculate the probability of catching a brown trout the second time

After catching and releasing one brown trout (since it's released, the total number of trouts is still 24), the probability of catching a brown trout the second time is also \(\frac{6}{24}=\frac{1}{4}\).

Step4: Calculate the probability of both events

Since the two catches are independent events, the probability of catching a brown trout each time is \(\frac{1}{4}\times\frac{1}{4}\).

$$ \frac{1}{4}\times\frac{1}{4}=\frac{1\times1}{4\times4}=\frac{1}{16} $$

Answer:

\(\frac{1}{16}\) (the second option)