The conditional relative frequency table was generated using data that compared the outside temperature each day to whether it rained that day.
Weather
| | Rain | No Rain | Total |
| :---- | :--- | :------ | :---- |
| $80^{\circ} F$ or Greater | 0.35 | 0.65 | 1.0 |
| Less than $80^{\circ} F$ | 0.3 | 0.7 | 1.0 |
| Total | \u2248 0.33 | \u2248 0.67 | 1.0 |
Given that it was less than $80^{\circ}$ on a given day, what is the probability that it also rained that day?
A. 0.3
B. 0.35
C. 0.65
D. 0.7
Answer (1)
The problem provides a conditional relative frequency table.
We identify the probability of rain given the temperature was less than 8 0 ∘ F .
The probability is found directly from the table.
The probability that it rained given that the temperature was less than 8 0 ∘ F is 0.3 .
Explanation
Understand the problem We are given a conditional relative frequency table that compares the outside temperature each day to whether it rained that day. We want to find the probability that it rained, given that the temperature was less than 8 0 ∘ F .
Find the probability from the table The table provides the conditional probabilities directly. We look for the intersection of 'Less than 8 0 ∘ F ' and 'Rain'. The value at this intersection is 0.3.
State the final answer Therefore, given that it was less than 8 0 ∘ F on a given day, the probability that it also rained that day is 0.3.
Examples
Understanding conditional probabilities helps in weather forecasting. For example, knowing the probability of rain given a certain temperature can help you decide whether to carry an umbrella. This is also applicable in other fields like finance, where you can estimate the probability of a stock price increasing given certain market conditions, or in medicine, where you can determine the likelihood of a patient developing a disease given certain risk factors.
