Final answer:
The probability of catching a trout first and then a second trout can be calculated using the number of trout in the lake and the total number of fish.
Step-by-step explanation:
To find the probability of catching a trout first and then a second trout, we need to consider the number of trout in the lake and the total number of fish. From the given information, there are 80 trout in the lake.
Since the fisherman is catching two fish, the probability of catching a trout first is 80/200 (total number of fish). After catching the first trout, there will be 79 trout remaining out of a total of 199 fish. So, the probability of catching a second trout is 79/199.
To find the overall probability, we multiply the two probabilities together:
P(Trout and Trout) = (80/200) * (79/199) = 0.19899497 or approximately 0.199