What is the probability that at least two students in our class share the same birthday?...
Let ?? be the probability that in a group of ? people, at least two share the same birthday. Assume there are 365 days in a year, and that all birthdays are equally likely. a) What is the probability that in a group of 2, 3, 4, or 5 people, at least two have the same birthday? ?2=? ?3=? ?4=? ?5=?
Twenty students are enrolled in a class. What is the probability that at least two students have the same birthday? Repeat the problem for a class size of seventy. Ignore leap years.
There are 36 students enrolled in this class. What is the probability that at least two of the students have the same birthday? (Ignore the possibility that someone might have been born on Feb. 29.)
Suppose there are n students in a class. Assume n ≤ 365, and all possible sequences of n birthdays are equally likely. We also assume that the birthday of a student is equally likely to be any one of the 365 days of the year (i.e., ignore leap years or seasonal variation in birth rate). (a) What is the probability that all n students have different birthdays? (b) Calculate this probability numerically when n = 23, 45, 65 and 70....
. In a class of 50 students, assuming every student has a birthday at random from one of the 365 days independently of each other, what is the expected number of days none of the students has a birthday on? What is the expected number of days that are the birthdays of exactly one student?
. Consider your class of 29 students. Calculate the probability that at least two students have the same birthday. For this purpose, assume each day of the year is represented by a box, and we place the name of the student in the box corresponding to their birthday. (a) List total number of possible arrangements. (b) List total number of arrangements that do not have two names in the same box. Obtain the probability that no two students have the...
(1 point) Consider the experiment, called the birthday problem, where our task is to determine the probability that in a group of people of a certain size there are at least two people who have the same birthday (the same month and day of month). Suppose there is a room with 10 people in it, find the probability that at least two people have the same birthday, Ignore leap years; assume each year has 365 days. Answer
Birthday Paradox: In a classroom of 30 students, what is the probability that at least two students share 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...