1- A poll of 500 people determines that 382 like ice cream and 362 like cake. Howmany people like both if each of them likes at least one of the two?

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Answered: many people like both if cach of them…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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You have 5 adult emus and 6 juvenile emus. How many ways are there to choose a group of emus so exactly 4 are adults and 2 are juveniles?
Let's say you have a weird relationship with a friend, where each week each of you can choose to either be a bad friend or a good friend. Then, each of you will get some amount of happiness according to the following table: You're a bad friend You're a good friend Your friend is a bad friend You get 5 happiness You get 10 happiness Your friend is a good friend You get +10 happiness You get +5 happiness 1. How would you choose whether to be a good or bad friend each week to maximize your happiness? What sort of strategy might you choose? Does it depend on what your friend chooses? We'd highly recommend looking at evolution of trust for some ideas on possible strategies. Note that you can change what you choose for different weeks.
Show that in a group of people there must be two individuals that have the same number of friends within the group.
At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the duck. There are a total of eight ducks with "Win" written on the underside of the duck, and there are 17 ducks with "Lose" written on the underside of the duck. After each pick, if a prize is won, the duck is replaced in the pond. If a prize is not won, then the duck is again placed back into the pond. If an individual makes four picks, what is the probability the individual will win a prize exactly one time? (4) (0.32) (0.68) 1! 4! (0.32)¹ (0.68)³ O2(0.32)(0.68) (0.32) (0.68)³
A shoe company wants to test an updated model of a running shoe on its wear after one month of running. Which of the following describes a matched pairs design? They recruit 50 people who run on a regular basis to participate in their study. They will have the runners wear the shoes when they run for two months. After two O The subjects are numbered 1-50, and these numbers are put into a random number generator. The first 25 random numbers, ignoring repeats, represent the subjects assigned to the new model group. The remaining 25 subjects will wear the original model. months, the wear on the shoes will be determined using the depth of the tread and flexibility of the toe box. The wear between the new model and the original model will then be compared. The subjects' names are written on equal-sized slips of paper and placed into a hat. A researcher then reaches in and pulls out 25 slips of paper. These subjects are assigned to the new model group. The remaining 25 subjects will be…
Jennifer, Bridget, Sandra, Robertina, and Joycelyn have their birthdays on consecutive days, but not necessarily in that order. Jennifer’s birthday is as many days before Sandra’s as Bridget’s is after Joycelyn’s. Robertina is two days older than Joycelyn. Sandra’s birthday this year is on a Wednesday. On what days of the week are the birthdays of the other four this year?

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many people like both if cach of them likes at least one of the two?