You ask a neighbor to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.85. With water it will die with probability 0.55. You are 89 % certain the neighbor will remember to water the plant.
You come back from the vacation and the plant is dead. What is the probability the neighbor forgot to water it?
Well....
I am not %100 percent sure, but I think I have got the right answer.
100-89%=11%
Then, 85% of 11% is 9% (rounded)
So I would say 9%
Does this question come form a section in your course called Markov's chains?
if so, then set up a transition matrix with 2 columns called Die, Live and
two rows called water, no water
that would be
.85 .15
.55 .45
multiply that by
.11 .89 -- did water is last number
to get
.58 .417
so there is a 58% chance your neighbour forgot to water.
both of you are wrong...
any one know the answer:(?
You need to use the rule of BAYES and the theorem of total probability.
To determine the probability that the neighbor forgot to water the plant given that it is dead, we can use Bayes' theorem.
Let's define the events:
A = Neighbor forgot to water the plant
B = Plant is dead
We want to find P(A|B) which represents the probability that the neighbor forgot to water the plant given that it is dead.
Bayes' theorem states:
P(A|B) = (P(B|A) * P(A)) / P(B)
Given information:
P(B|A) = 1 - probability that the plant survives without water = 1 - 0.85 = 0.15
P(B|not A) = 1 - probability that the plant survives with water = 1 - 0.55 = 0.45
P(A) = probability that the neighbor forgot to water the plant = 1 - probability that the neighbor remembered to water the plant = 1 - 0.89 = 0.11
P(not A) = probability that the neighbor remembered to water the plant = 0.89
To calculate P(B), we need to consider two cases:
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
= 0.15 * 0.11 + 0.45 * 0.89
Now we can substitute these values back into Bayes' theorem:
P(A|B) = (P(B|A) * P(A)) / P(B)
P(A|B) = (0.15 * 0.11) / (0.15 * 0.11 + 0.45 * 0.89)
After calculating the expression above, we find that P(A|B) is approximately 0.0323. Therefore, the probability that the neighbor forgot to water the plant given that it is dead is approximately 0.0323 or 3.23%.