In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data ...

Question

In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 25 degrees C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 25 degrees C, or below 25 degrees C. What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 25 degrees C?

A. 0.4
B. 0.6
C. 0.8
D. 0.9

Accepted Answer

0.8 (Option C) We are given the total probability of rain and the conditional probability of rain when temperature is at most 25 degrees. Since temperature is equally split above/below 25 degrees, we can use the Law of Total Probability to find the unknown conditional probability of rain when temperature is above 25 degrees. The two conditional probabilities must average out to give the overall probability.