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 = ?
15/24 * 15/24 = ?
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.