Subjects statistics

Conditional Rain Probability 9922E9

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1. The problem asks: Given that it was less than 80˚F on a given day, what is the probability that it also rained that day? 2. This is a conditional probability problem. The formula for conditional probability is: $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$ where $P(A|B)$ is the probability of event A given event B, $P(A \cap B)$ is the probability of both A and B happening, and $P(B)$ is the probability of event B. 3. Here, event A is "it rained," and event B is "temperature less than 80˚F." 4. From the table, the conditional relative frequency of rain given less than 80˚F is 0.3. This means: $$P(\text{Rain} | \text{Less than 80˚F}) = 0.3$$ 5. Therefore, the probability that it rained given the temperature was less than 80˚F is 0.3. Final answer: 0.3