Probability of Rainy Days

In a certain city, the probability of rain on any given day is 0.3. If the weather forecast predicts rain for 3 consecutive days, what is the probability that it actually rains on at least 2 out of these 3 days?

Let $X$ be the random variable representing the number of days it rains out of the 3 days. Then, $X$ follows a binomial distribution, where the number of trials $n = 3$ and the probability of success (rain) on any given day $p = 0.3$. We can calculate the probability of at least 2 rainy days using the formula for binomial probabilities.

The probability mass function for a binomial random variable is given by:

$$ P(X = k) = {n race k} p^k (1-p)^{n-k} $$

for $k = 0, 1, 2, ext{ and } n$.