Question

The probability that a region prone to hurricanes will be hit by a hurricane in any single year is 1/5. What is the probability of a hurricane at least once in the next five years?

Answer 1

At least 1 hit means 1, 2, 3, 4, or 5 hits in the 5-year period.
To compute this, you could compute five different binomial probabilities and sum them.
Or, rememembering that P(0 hits) + P(at least 1 hit) = 1, you could compute P(at least 1 hit) by subtracting P(0 hits) from 1.
P(at least 1 hit) = 1 - P(0 hits) = 1 - C(5,0) * (4/5)^0 * (1/5)^5 = 1 - 1*1* 1 / 3125.
1 - .00032 = .99968 as the probability of at least 1 hit within a five year period.