Final answer:
The probability of four consecutive rainy days with a 40% chance of rain each day is 2.56%, calculated by raising 0.40 to the fourth power.
Step-by-step explanation:
The probability of four rainy days in a row when the forecast calls for a "40% chance of rain" each day is calculated by multiplying the probability of rain for each day together. Since the days are independent events, if the probability of rain on any given day is 0.40, then we must take 0.40 to the fourth power to determine the probability of it raining four days in a row.
The calculation is as follows: 0.40 * 0.40 * 0.40 * 0.40 = 0.0256.
Therefore, the probability of experiencing four consecutive rainy days under these conditions is 2.56%.
It is important to understand that probabilities are not simply additive, as shown in incorrect statements where the probability exceeds 100%, and the concept of a confidence interval in polls which quantifies the uncertainty around a sample statistic.