In a certain town, the probability that it will rain in the afternoon is known…
2006
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°C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 25°C, or at/below 25°C. What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 25°C?
- A.
0.4
- B.
0.6
- C.
0.8
- D.
0.9
Attempted by 11 students.
Show answer & explanation
Correct answer: C
Solution: Use the law of total probability to relate the unconditional probability of rain to the two conditional probabilities.
Let p = probability it rains in the afternoon given the noon temperature is above 25°C.
Given: overall P(rain) = 0.6, P(rain | temperature ≤ 25°C) = 0.4, and P(temperature ≤ 25°C) = 0.5 (so P(temperature > 25°C) = 0.5).
Apply total probability: 0.6 = 0.4·0.5 + p·0.5.
Compute: 0.6 = 0.2 + 0.5p ⇒ 0.4 = 0.5p ⇒ p = 0.8.
Answer: 0.8 is the probability it will rain in the afternoon when the noon temperature is above 25°C.