Question

In: Statistics and Probability

Before each class, I either drink a cup of coffee, a cup of tea, or a...

Before each class, I either drink a cup of coffee, a cup of tea, or a cup of water. The probability of coffee is 0.7, the probability of tea is 0.2, and the probability of water is 0.1. If I drink coffee, the probability that the lecture ends early is 0.3. If I drink tea, the probability that the lecture ends early is 0.2. If I drink water, the lecture never ends early.
1) What’s the probability that I drink tea and finish the lecture early?
2) What’s the probability that I finish the lecture early?
3) Given the lecture finishes early, what’s the probability I drank coffee?

Solutions

Expert Solution

The probability of coffee, P[ Coffee ] = 0.7

The probability of tea, P[ Tea ] = 0.2

The probability of water, P[ Water ] = 0.1

P[ I drink coffee, the lecture ends early ] = P[ lecture ends early | coffee ] =  0.3

P[ I drink tea, the lecture ends early ] = P[ lecture ends early | tea ] =  0.2

P[ I drink water, the lecture ends early ] = P[ lecture ends early | water ] =  0

1) What’s the probability that I drink tea and finish the lecture early?

P[ I drink tea and finish the lecture early ] = P[ lecture ends early | tea ]*P[ Tea ]

P[ I drink tea and finish the lecture early ] = 0.2*0.2

P[ I drink tea and finish the lecture early ] = 0.04

2) What’s the probability that I finish the lecture early?

P[ I finish the lecture early ] = P[ I drink coffee and finish the lecture early ] + P[ I drink tea and finish the lecture early ] + P[ I drink water and finish the lecture early ]

P[ I drink coffee and finish the lecture early ] = P[ lecture ends early | coffee ]*P[ Coffee ]

P[ I drink coffee and finish the lecture early ] = 0.7*0.3

P[ I drink coffee and finish the lecture early ] = 0.21

P[ I drink tea and finish the lecture early ] = P[ lecture ends early | tea ]*P[ Tea ]

P[ I drink tea and finish the lecture early ] = 0.2*0.2

P[ I drink tea and finish the lecture early ] = 0.04

P[ I drink water and finish the lecture early ] = P[ lecture ends early | water ]*P[ Water ]

P[ I drink water and finish the lecture early ] = 0.1*0

P[ I drink water and finish the lecture early ] = 0

P[ I finish the lecture early ] = 0.21 +0.04 + 0

P[ I finish the lecture early ] = 0.25

3) Given the lecture finishes early, what’s the probability I drank coffee?

P[ I drank coffee | the lecture finishes early ] = P[ I drink coffee and finish the lecture early ]/P[ I finish the lecture early ]

P[ I drank coffee | the lecture finishes early ] = 0.21/0. 25

P[ I drank coffee | the lecture finishes early ] = 0.84

orchestra answered 1 year ago
Next > < Previous

Related Solutions

In a population of interest, we know that, 77% drink coffee, and 23% drink tea. Assume...
In a population of interest, we know that, 77% drink coffee, and 23% drink tea. Assume that drinking coffee and tea are disjoint events in this population. We also know coffee drinkers have a 30% chance of smoking. There is a 13% chance of smoking for those who drink tea. Five individuals are randomly chosen from this population. What is the probability that four of them drink coffee? Five individuals are randomly chosen from this population. What is the probability...
Assume you drank a cup of coffee or tea this morning. Did you make it yourself...
Assume you drank a cup of coffee or tea this morning. Did you make it yourself or did you buy it? Draw a detailed process map illustrating the activity involved in making/obtaining your beverage. Use the appropriate process symbols. Be sure to take into account decision points and input and outputs. Explain the decision points and processes involved.
Survey question: Do you prefer tea or coffee as a mid-afternoon hot drink?•Findings: tea = 20%,...
Survey question: Do you prefer tea or coffee as a mid-afternoon hot drink?•Findings: tea = 20%, coffee = 80% and n = 150 •Fill in the sentence: We found that ____% of the sample ___________________. We are very confident that if the survey is repeated a large number of times, 95% of the findings will fall in the range of _____% and _____%.
coin-operated drink machine was designed to discharge a mean of 7ounces of coffee per cup. In...
coin-operated drink machine was designed to discharge a mean of 7ounces of coffee per cup. In a test of the machine, the discharge amounts in14 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 7.02 ounces and 0.17 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.05 level of significance, to conclude that the true mean discharge, μ , differs from...
Your 300mL cup of coffee is too hot to drink when served at 90.0 ∘C. A)What...
Your 300mL cup of coffee is too hot to drink when served at 90.0 ∘C. A)What is the mass of an ice cube, taken from a -16.0 ∘C freezer, that will cool your coffee to a pleasant 58.0 ∘?
Objective: Create a program that has a class to represent a cup of coffee that combines...
Objective: Create a program that has a class to represent a cup of coffee that combines the properties: name and caffeine content. The class should also have a method that calculates the number of cups that would be maximally risky to consume in a short period of time. The program should create two instances of the class coffee where the user enters their properties and should output the amount of coffees that consumed would be risky. Requirements: Write a class...
Objective: Create a program that has a class to represent a cup of coffee that combines...
Objective: Create a program that has a class to represent a cup of coffee that combines the properties: name and caffeine content. The class should also have a method that calculates the number of cups that would be maximally risky to consume in a short period of time. The program should create two instances of the class coffee where the user enters their properties and should output the amount of coffees that consumed would be risky. Requirements: Write a class...
Consumers choose between coffee and tea. Tea is known to be healthier than coffee but coffee...
Consumers choose between coffee and tea. Tea is known to be healthier than coffee but coffee has more caffeine. Consumers have decreasing marginal utility for both caffeine and health. However, recent scientific results find that coffee is much healthier for you than previously believed. Answer the following questions: 1. Show graphically and explain in 2-3 sentences how this discovery impacts the equilibrium Price and Quantity in the perfectly competitive coffee market. 2. Show graphically and explain in 2-3 sentences how...
Consumers choose between coffee and tea. Tea is known to be healthier than coffee but coffee...
Consumers choose between coffee and tea. Tea is known to be healthier than coffee but coffee has more caffeine. Consumers have decreasing marginal utility for both caffeine and health. However, recent scientific results find that coffee is much healthier for you than previously believed. Answer the following questions: 1. Based on economic theory, show graphically (budget constraint and indifference curves) and explain in 2-3 sentences how this scientific evidence will change a consumer’s choice decision. 2. Using the multiattribute model,...
1. I have 250 g of tea at 90°C in a light foam cup. I have...
1. I have 250 g of tea at 90°C in a light foam cup. I have some ice cubes at 0°C, each with a mass of 10 g. How many should I add to my tea to make it drinkable? Explain your assumptions. 2. A thermos will keep hot things hot or cold things cold by preventing the transfer of heat. Explain how a thermos prevents each of the different kinds of heat transfer. 3. I have 5.0 liters of...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT