3. You live next door to a meteorologist and you never pay attention to her weather reports, but because you leave in the morning at the same time, you always notice whether she carries an umbrella to work. For kicks you kept track of umbrella days and rainy days. Here's what you observed: Of the 60 days that it rained she canied her umbrella 45 times. 0f the 130 days that it didn't rain she carried her umbrella only 15 times. Based on this small experiment: a. What is the probability of rain? b. Think of your neighbor as a diagnostic test and the umbrella as a positive indication of rain. What is your neighbor's false positive rate? e. What is your neighbor's false negative rate? d. What is the conditional probability that your neighbor carries an umbrella given that it rains? e. What is the probability that your neighbor doesn't carry an umbrella given that it doesn't rain? f. What is the probability that it will rain given that your neighbor carries an umbrella? g. What is the probability that it will not rain given that your neighbor does not carry an umbrella