A pond is freshly stocked with 15 brown trout and 9 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?
25/64
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
15/24 * 15/24 = ?
To find the probability that the fisherman caught a brown trout each time, we need to consider the total number of trout in the pond and the number of brown trout remaining after each catch.
Initially, there are 15 brown trout and 9 lake trout in the pond, for a total of 15 + 9 = 24 trout.
After the fisherman catches and releases a trout, there are now 23 trout remaining, consisting of 15 brown trout and 8 lake trout. The probability of catching a brown trout the first time is therefore 15/23.
After some time passes and the fisherman catches another trout, there are now 22 trout remaining, with 14 brown trout and 8 lake trout. The probability of catching a brown trout for the second time is 14/22.
To find the probability of both events happening (catching a brown trout each time), we can multiply the individual probabilities together:
(15/23) * (14/22) = 210/506.
Therefore, the probability that the fisherman caught brown trout each time is 210/506, or approximately 0.414.