Final answer:
To calculate the probability that in 5 non-overlapping 12-minute periods, exactly one moderate weather warning is announced, we can use the binomial distribution formula.
Step-by-step explanation:
To calculate the probability that in 5 non-overlapping 12-minute periods, exactly one moderate weather warning is announced, we need to use the binomial distribution formula.
The probability of success, which in this case is the probability that a moderate weather warning is announced in a 12-minute period, can be calculated as 1/7 since there are 7 possible outcomes (from 6 to 7 lightning strikes) and we want to find the probability of 1 success.
The formula for the probability of exactly one success in a given number of trials is:
P(X = k) = nCk * p^k * (1-p)^(n-k)
Where n is the number of trials, k is the number of successes, p is the probability of success, and nCk is the number of ways to choose k objects from a set of n objects.
In this case, n is 5, k is 1, and p is 1/7. Plugging in these values, we can calculate:
P(X = 1) = 5C1 * (1/7)^1 * (6/7)^4
Simplifying gives:
P(X = 1) = 5 * (1/7) * (6/7)^4
Calculating this expression gives the probability that exactly one moderate weather warning is announced in 5 non-overlapping 12-minute periods.