Answer:
(a) The probability is 0.785
(b) The probability is 0.3721
Step-by-step explanation:
Let's call A the event that the plant is alive, D the event that the plant die, W the event that your neighbor remember to water the plant and NW the event that your neighbor doesn't remember to water the plant.
The probability P(A) that the plant will be alive when you return is calculate as the sum of:
P(A) = P(W∩A) + P(NW∩A)
So, the probability P(W∩A) that your neighbor water the plant and it is alive is calculate as:
P(W∩A) = 0.9 * 0.85 = 0.765
Where 0.9 is the probability that your neighbor remember to water the plant and 0.85 is equal to (1-0.15) and it is the probability that the plant is alive given that the plant was water.
At the same way, the probability P(NW∩A) that the neighbor didn't water the plant and it is alive is calculate as:
P(NW∩A) = 0.1 * 0.2 = 0.02
Then, P(A) is:
P(A) = 0.765 + 0.02 = 0.785
On the other hand, the probability P(NW/D) that your neighbor forgot to water the plant given that is dead is:
P(NW/D) = P(NW∩D)/P(D)
Where P(D) = P(W∩D) + P(NW∩D)
So, the probability P(W∩D) that the neighbor water the plant and it dies and the probability P(NW∩D) that the neighbor didn't water the plant and it dies are calculate as:
P(W∩D) = 0.9 * 0.15 = 0.135
P(NW∩D) = 0.1 * 0.8 = 0.08
Then, P(D) is:
P(D) = 0.135 + 0.08 = 0.215
Finally, P(NW/D) is:
P(NW/D) = 0.08/0.215 = 0.3721