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#6 You go to a party which has 1000 guests (including you). a) What is the...
Suppose you are one of 17p eople at a dinner party. Find the probability that at...
Suppose you are one of 17p eople at a dinner party. Find the probability that at least one of the other guests has the same birthday as you and that some pair of guests share the same birthday. Assume there are 365 days in the year. The probability that at least one other guest shares your birthday is approximately _____(Round to four decimal places as needed.) The probability that some pair of guests share the same birthday is approximately _____(Round...
Chapter 2.2 Questions l. You are having a party, and have the guests choose out of...
Chapter 2.2 Questions l. You are having a party, and have the guests choose out of a box of goodies at randonm. There are 2 party hats (H), 3 yo-yos (Y), and 1 box of turtle chocolates (T) (a) Construct a tree diagram for two guests choosing 1 goody each from the bag. Give yourself lots of room to draw it. (b) What is the probability of choosing at least one party hat? (c) What is the probability of no...
Suppose you are organizing a dinner party. The guests are going to be seated around a single roun...
Suppose you are organizing a dinner party. The guests are going to be seated around a single roundtable. Show that if each guest knows at least half of the other guests, then everyone can be seated next to two people they know.
Guests are arriving at a party at a rate of 12 per minute. Each guest will...
Guests are arriving at a party at a rate of 12 per minute. Each guest will be checked in, served a drink, and accompanied to his/her table by one receptionist, one bartender, and one usher respectively. Both the receptionist and usher can serve 10 guests per minute, whereas the bartender takes 5 minutes to serve one guest. Which resource is the bottleneck and what is the process capacity in guests per minute? (a) Bartender, 0.2 (b) Bartender, 5 ...
Birthday problem). Assume that a host invites n guests and that days of all n+1 people...
Birthday problem). Assume that a host invites n guests and that days of all n+1 people are independent and uniformly distributed acros Exercise 1.10 ( the birth all the 365 days of the year 1. Prove the following: The probability that two of the guests share the same birth- day is larger than one-half if and only if n 2 23. 2. How large should n be so that the probability that at least one of the guests has the...
i need a clear explanation . 2. Consider a group of 3 students. Each student has...
i need a clear explanation .
2. Consider a group of 3 students. Each student has a birthday that can be any one of the days numbered 1,2,3,...,365. (a) What is the probability that exactly two of them have the same birthday? (b) What is the probability that exactly two of them have the same birthday given that at least two students have the same birthday?
4. For the following problem, ignore the year of birth while comparing two birthdays. Moreover, assume...
4. For the following problem, ignore the year of birth while comparing two birthdays. Moreover, assume that the year is exactly 365 days (ignore the 29th of February) Note that matching birthdays means the birthdays are the same (a) You are a member of a class room that has n +1 students including you. What is the probability that you find at least one student, other than you, who has a birthday that matches yours? (b) In another classroom that...
4. For the following problem, ignore the year of birth while comparing two birthdays. Moreover, assume...
4. For the following problem, ignore the year of birth while comparing two birthdays. Moreover, assume that the year is exactly 365 days (ignore the 29th of February) Note that matching birthdays means the birthdays are the same (a) You are a member of a class room that has n 1 students including you. What is the probability that you find at least one student, other than you, who has a birthday that matches yours? (b) In another classroom that...
You are at a cocktail party and one of the guests says to you, “Oh, you...
You are at a cocktail party and one of the guests says to you, “Oh, you are learning about cancer in Cell and Molecular Biology? Well, I’ve gotta tell you-- I think it’s all a big shakedown. These researchers and doctors have been trying to cure cancer for more than 50 years and there’s still no cure for cancer. What a rip off for good, hard working tax payers like myself!” How would you respond?
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a...
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse? Hint. Label the seats, the individuals, and the couples. There are 6! 720 seating arrangements altogether. Apply inclusion-exclusion to the events A, [ith couple sit next to each other),-1, 2, 3. Count carefully the numbers of arrangements in...
Chapter 2.2 Questions l. You are having a party, and have the guests choose out of a box of goodies at randonm. There are 2 party hats (H), 3 yo-yos (Y), and 1 box of turtle chocolates (T) (a) Construct a tree diagram for two guests choosing 1 goody each from the bag. Give yourself lots of room to draw it. (b) What is the probability of choosing at least one party hat? (c) What is the probability of no...
Birthday problem). Assume that a host invites n guests and that days of all n+1 people are independent and uniformly distributed acros Exercise 1.10 ( the birth all the 365 days of the year 1. Prove the following: The probability that two of the guests share the same birth- day is larger than one-half if and only if n 2 23. 2. How large should n be so that the probability that at least one of the guests has the...
i need a clear explanation .
2. Consider a group of 3 students. Each student has a birthday that can be any one of the days numbered 1,2,3,...,365. (a) What is the probability that exactly two of them have the same birthday? (b) What is the probability that exactly two of them have the same birthday given that at least two students have the same birthday?
4. For the following problem, ignore the year of birth while comparing two birthdays. Moreover, assume that the year is exactly 365 days (ignore the 29th of February) Note that matching birthdays means the birthdays are the same (a) You are a member of a class room that has n +1 students including you. What is the probability that you find at least one student, other than you, who has a birthday that matches yours? (b) In another classroom that...
4. For the following problem, ignore the year of birth while comparing two birthdays. Moreover, assume that the year is exactly 365 days (ignore the 29th of February) Note that matching birthdays means the birthdays are the same (a) You are a member of a class room that has n 1 students including you. What is the probability that you find at least one student, other than you, who has a birthday that matches yours? (b) In another classroom that...
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse? Hint. Label the seats, the individuals, and the couples. There are 6! 720 seating arrangements altogether. Apply inclusion-exclusion to the events A, [ith couple sit next to each other),-1, 2, 3. Count carefully the numbers of arrangements in...
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