Question

19 historically, a given day at the beginning of march in upstate new york has an 18% chance of snow and a 12% chance of rain. if there is a 4% chance it will rain and snow on a day, and a random day at the beginning of march is selected, find the p(snow|rain).
a 22%
b 33%
c 49%
d 26%

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \), where \( A \) is the event "snow" and \( B \) is the event "rain".

Step2: Identify Given Probabilities

We know that \( P(\text{rain and snow}) = P(A \cap B) = 4\% = 0.04 \) and \( P(\text{rain}) = P(B) = 12\% = 0.12 \).

Step3: Apply the Formula

Substitute the values into the formula: \( P(\text{snow}|\text{rain}) = \frac{P(\text{snow} \cap \text{rain})}{P(\text{rain})} = \frac{0.04}{0.12} \).
Simplify the fraction: \( \frac{0.04}{0.12} = \frac{4}{12} = \frac{1}{3} \approx 0.3333 \), which is \( 33\% \).

Answer:

B. 33%