Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
In a town where 1/5 of the days are sunny and 4/5 are cloudy, the next four days are all sunny.
The individual events (days being sunny or cloudy) are independent because the probability of one day being sunny or cloudy does not affect the probability of another day being sunny or cloudy.
To find the combined probability of the next four days being sunny, we need to multiply the probability of each day being sunny together. Since the probability of a sunny day is 1/5, the probability of four consecutive sunny days is:
(1/5) * (1/5) * (1/5) * (1/5) = 1/625