Explanation:
If the probability of a miracle occurring within the next 1,000 years is 0.99, it means that the probability of a miracle not occurring within the next 1,000 years is 1 - 0.99 = 0.01.
Now, let's calculate the probability that there will be a miracle within the next 200 years. Since the time of the next occurrence of a miracle is independent of the last occurrence, we can use the complement probability to find the probability of no miracle occurring in the next 200 years and then subtract it from 1 to get the probability of a miracle occurring.
The probability of no miracle occurring in the next 200 years is equivalent to the probability of no miracle occurring in the first 200 years followed by no miracle occurring in the next 800 years (since we have a 1,000-year window).
Probability of no miracle in the first 200 years = 0.01
Probability of no miracle in the next 800 years = 0.01
Now, we can calculate the overall probability of no miracle in the next 1,000 years:
Probability of no miracle in the next 1,000 years = (Probability of no miracle in the first 200 years) * (Probability of no miracle in the next 800 years) = 0.01 * 0.01 = 0.0001
Finally, to find the probability of a miracle occurring within the next 200 years, we subtract this probability from 1:
Probability of a miracle within the next 200 years = 1 - Probability of no miracle in the next 1,000 years = 1 - 0.0001 = 0.9999
So, the probability that there will be a miracle within the next 200 years is approximately 0.9999, or 99.99%.