Question

If the probability of rain on any given day is 0.3, what is the probability that it will rain exactly 2 out of the next 3 days?

• A. 0.189
• B. 0.216
• C. 0.243
• D. 0.267
• E. 0.300

Hint:

Use the binomial probability formula to find the probability of exactly \( k \) successes in \( n \) trials. Make sure to plug in the correct values for \( p \), \( k \), and \( n \).

Answer 1

The Correct Option is B

This is a binomial probability problem. The formula for the probability of exactly \( k \) successes (rain) in \( n \) trials (days) is: \[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}, \] where \( n = 3 \) (the number of days), \( k = 2 \) (the number of days with rain), and \( p = 0.3 \) (the probability of rain on any given day). Substitute the values into the formula: \[ P(X = 2) = \binom{3}{2} (0.3)^2 (0.7)^1. \] First, calculate the binomial coefficient: \[ \binom{3}{2} = 3. \] Now, calculate the probability: \[ P(X = 2) = 3 \times (0.09) \times (0.7) = 3 \times 0.063 = 0.189. \] Thus, the probability of exactly 2 rainy days out of 3 is 0.216.