Probability of Rain Over Given Days

In a certain city, the probability that it rains on a given day is 0.4. If the weather is independent from day to day, what is the probability that it will rain on exactly 3 out of the next 5 days?

To solve this, use the binomial probability formula:

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

where:

• $$ n $$ = total number of trials (days)
• $$ k $$ = number of successes (rainy days)
• $$ p $$ = probability of success on an individual trial (rain)