Suppose that, historically, April has experienced rain and a temperature between 35 and 50 degrees on 20 days.Also, historically, the month of April has had a temperature between 35 and 50 degrees on 25 days.You have scheduled a golf tournament for April 12.If the temperature is between 35 and 50 degrees on that day, what will be the probability that the players will get wet?
A)0.333
B)0.667
C)0.800
D)1.000

Question

Quizplus · Accepted Answer

The probability of rain given that the temperature is between 35 and 50 degrees can be calculated using Bayes' theorem as follows: 
P(rain | temperature between 35 and 50) = P(temperature between 35 and 50 | rain) * P(rain) / P(temperature between 35 and 50)
We are given that historically, April has experienced rain and a temperature between 35 and 50 degrees on 20 days, and that the month of April has had a temperature between 35 and 50 degrees on 25 days. Therefore, 
P(temperature between 35 and 50 | rain) = 20/20 = 1 (if it rains, the temperature is definitely between 35 and 50 degrees)
P(rain) = 20/30 = 2/3 (out of 30 days in April, it has historically rained on 20 days)
P(temperature between 35 and 50) = 25/30 (out of 30 days in April, the temperature has historically been between 35 and 50 degrees on 25 days)
Plugging in these values into Bayes' theorem, we get:
P(rain | temperature between 35 and 50) = 1 * (2/3) / (25/30) = 0.8
Therefore, the probability of players getting wet if the temperature is between 35 and 50 degrees on April 12 is 0.8, or 80%.

Suppose That, Historically, April Has Experienced Rain and a Temperature