Suppose that a fisherman has a 0.16 probability of catching a fish on any day he goes out fishing.
What is the probability of him catching at least one fish during a 9 day period?
To find the probability of the fisherman catching at least one fish during a 9-day period, we need to calculate the probability of the complement event, which is the event of the fisherman not catching any fish during the 9 days.
The probability of the fisherman not catching a fish on any given day is 1 - 0.16 = 0.84.
Since the fishing days are independent events, we can multiply the probabilities:
Probability of not catching a fish in 9 days = (0.84)(0.84)(0.84)(0.84)(0.84)(0.84)(0.84)(0.84)(0.84) ≈ 0.1934.
Therefore, the probability of the fisherman catching at least one fish during a 9-day period is 1 - 0.1934 = 0.8066, or approximately 80.66%.