Answer: The probability that the plant will be alive when you return is approximately 0.785, or 78.5%.
Explanation:
Let's break down the probabilities based on the different scenarios:
The plant is watered:
Probability of the plant dying: 0.15
The plant is not watered:
Probability of the plant dying: 0.8
Since you're 90% certain that your neighbor will remember to water the plant, the probabilities of the two scenarios need to be weighted accordingly:
Probability that the plant is watered: 0.9
Probability that the plant is not watered: 0.1
Now, let's calculate the overall probability that the plant will be alive when you return:
Probability (Plant Alive) = Probability (Plant Watered) * Probability (Plant Survives when Watered) + Probability (Plant Not Watered) * Probability (Plant Survives when Not Watered)
Probability (Plant Alive) = (0.9 * (1 - 0.15)) + (0.1 * (1 - 0.8))
Probability (Plant Alive) = (0.9 * 0.85) + (0.1 * 0.2)
Probability (Plant Alive) = 0.765 + 0.02
Probability (Plant Alive) = 0.785
So, the probability that the plant will be alive when you return is approximately 0.785, or 78.5%.