Answer:
If the first e-mail you got from sensor S indicates a daily high over 80 degrees, the probability that the sensor is placed in Maine = 0.01156
Step-by-step explanation:
Let the probability of placing the sensor S at Maines be P(M) = 0.05
Probabilty of placing the sensor S in the Sahara desert = P(S) = 1 - P(M) = 1 - 0.05 = 0.95 (this is because the meteorologist is confident that the sensor is at either of the two places.
Let the probability of a high temperature of 80 degrees or more = P(T)
Probability of the sensor picking up temperature of 80 degrees or more given that it is in Maine = P(T|M) = 20% = 0.20
Probability of the sensor picking up temperature of 80 degrees or more given that it is in the Sahara desert = P(T|S) = 90% = 0.90
From the definition of rhe conditional probability
P(A|B) = P(A n B) ÷ P(B)
P(A n B) = P(A|B) × P(B)
If the first e-mail you got from sensor S indicates a daily high over 80 degrees, what is the probability that the sensor is placed in Maine?
The required probability = P(M|T)
P(M|T) = P(M n T) ÷ P(T)
P(T) = P(M n T) + P(S n T)
P(M n T) = P(T|M) × P(M) = 0.20 × 0.05 = 0.010
P(S n T) = P(T|S) × P(S) = 0.90 × 0.95 = 0.855
P(T) = 0 010 + 0.855 = 0.865
P(M|T) = P(M n T) ÷ P(T)
P(M|T) = (0.010/0.865) = 0.01156
Hope this Helps!!!
