Question

you ask your neighbor to water a sickly plant while you are on vacation. without water it will die with probability .8; with water it will die with probability .15. you are 90 percent certain that your neighbor will remember to water the plant. what is the probability that the plant will be alive when you return?

Answer 1

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%.