Since you are away on vacation, you ask your roommate to water an ornery plant.
ID: 3153624 • Letter: S
Question
Since you are away on vacation, you ask your roommate to water an ornery plant. If your roommate remembers to water the plant, it will live with a probability of 0.90,while if your roommate forgets to water the plant, it only has a 0.05 chance of living. Your roommate has an 85% chance of remembering to water the plant. In showing your work below, let W represent the event that your roommate waters the plant, and let L represent the event that the plant lives.
A) What is the probability that your roommate remember to water the plant and it lives?
B)What is the probability that the plant lives?
C)If the plant lives, what is the probability that your roommate remembered to water it?
D) Find P(W union L). The union is the upside down U that represents or.
Explanation / Answer
a)
P(W n L) = P(W) P(L|W) = 0.85*0.90 = 0.765 [ANSWER]
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b)
Note that by Bayes' Rule,
P(L) = P(W) P(L|W) + P(W') P(L|W') = 0.85*0.90 + (1-0.85)*0.05 = 0.7725 [ANSWER]
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c)
Hence,
P(W|L) = P(W n L)/P(L) = 0.765/0.7725 = 0.990291262 [ANSWER]
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d)
Hence,
P(W U L) = P(W) + P(L) - P(W n L) = 0.85 + 0.7725 - 0.765 = 0.8575 [ANSWER]