Question

In: Statistics and Probability

At Elmo’s, an old-fashioned barber shop in Melbourne, FL, 70% of all customers get a haircut,...

At Elmo’s, an old-fashioned barber shop in Melbourne, FL, 70% of all customers get a haircut, 40% get 3. At Elmo’s, an old-fashioned barber shop in Melbourne, FL, 70% of all customers get a haircut, 40% get a shave, and 95% get a haircut or a shave. Let A = customer gets a haircut and B = customer gets a shave.

a. Draw a Venn diagram showing the relationship between the events A and B. (4 points)

b. What is the probability that a randomly selected customer gets both a haircut and a shave? _________________________________(3)

c. What is the probability that a randomly selected customer a haircut or a shave, but not both? _________________________________(3)

d. What is the probability that a randomly selected customer gets a shave, given that he gets a haircut? ________________________________

Solutions

Expert Solution


Related Solutions

Ethan got a bad haircut from Sideshow Bob's Barber Shop. It did great harm to his...
Ethan got a bad haircut from Sideshow Bob's Barber Shop. It did great harm to his self-esteem and a sympathetic jury awarded him damages, and gave him this choice: He can either receive $85,000 per year for 10 years or $500,000 as a lump sum payment today. If his required rate of return is 12%, what should he do, and why? Group of answer choices He should reject the lump sum payment because the sum of the annuity payments is...
Campus Barber Shop has one barber. Customers arrive at a rate of 2.2 per hour, and...
Campus Barber Shop has one barber. Customers arrive at a rate of 2.2 per hour, and haircuts are given at a rate of 3 per hour. Assume the basic Poisson-Exponential model and answer the following questions. What is the probability that the barber is idle? What is the probability that one customer is getting a haircut and no one is waiting in the line? What is the probability that one customer is receiving a haircut and one customer is in...
A barber shop has two barbers, both of whom average 15 minutes/haircut (exponentially distributed). The first...
A barber shop has two barbers, both of whom average 15 minutes/haircut (exponentially distributed). The first customer Joe arrives when both barbers are free and starts his haircut. A second customer Jack arrives 10 minutes later while Joe is still getting his haircut. Finally, a third customer John arrives another 20 minutes later, while both Joe and Jack are still having their haircuts. Assuming that no other customers arrive in this 30-minute interval: a. What is the probability that Joe...
Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1...
Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1 customers per hour, and haircuts are given with a service rate of 5 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places. P0 = What is the probability that one customer is receiving a haircut and no...
Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1...
Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places. P0 = ????? What is the probability that one customer is receiving a haircut and...
A barber shop has an average of 12 customers between 8.00am and 9.00am every Saturday. Customers arrive according to Poisson distribution. Let X represent the time between arrivals.
A barber shop has an average of 12 customers between 8.00am and 9.00am every Saturday. Customers arrive according to Poisson distribution. Let X represent the time between arrivals. (a) Construct the distribution for the random variable X? (b) Find the mean and standard deviation of X. (c) What is the probability that the time between consecutive arrivals (customers) will fall between 3 and 6 minutes?
At a certain coffee​ shop, all the customers buy a cup of coffee and some also...
At a certain coffee​ shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 330 cups and a standard deviation of 23 cups. He also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 170 doughnuts and a standard deviation...
At a certain coffee​ shop, all the customers buy a cup of coffee and some also...
At a certain coffee​ shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 340 cups and a standard deviation of 18 cups. He also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 180 doughnuts and a standard deviation...
Stop and Shop grocery shops Incorporation study showed that 50% of all customers will return to...
Stop and Shop grocery shops Incorporation study showed that 50% of all customers will return to the same grocery shop. Suppose six customers are selected at random, what is the probability that: (a) Exactly two customers will return? (b) All six customers will return? (c) At least five customers will return? (d) At least one customer will return? (e) How many customers would be expected to return to the same store?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT