. In a class of 50 students, assuming every student has a birthday at random from...
What is the probability that at least two students in our class share the same birthday? Assuming that: Birthdays follow a uniform distribution. We have 35 students in our class! No one was born in a leap year. There are 365 days in a year!
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...
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?
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....
There are 12 female students and 18 male students in a class. Every student independently has a probability 0.3 of being a Math major. There are 14 Math majors in the class. Find the probability that among the Math majors, 6 students are female.
15. We flip a fair coin three times; these flips are independent of each other. These three coin flips give us a sequence of length three, where each symbol is H or T. Define the events A- B = "the sequence contains at most one T. "the symbols in the sequence are not all equal" Which of the following is true? (a) The events A and B are independent. (b) The events A and B are not independent (c) None...
Exercise 5. (13pt) Consider a class of 16 students. Every week 4 students have to give presentation. At the end of the course, each pair of students has done exactly one presentation together (1) How many weeks does the course have? (Hint: use double counting) (4pt) (2) How can you interpret this as a block system? (4pt) (3) What is the total number of block in this system and what does it represent? Compare this to your answer in par...
Dr. Campbell's MLA class has 15 students. All of the students know each other well, and each knows exactly what day of the week they were born on. What is the minimum number of students Dr. Campbell needs to randomly select to guarantee she has chosen two who were born on the same day? (Assume Dr. Campbell is not privy to their birthday information.)
4. Let X be the number of distinct birthdays in a group of 100 people. In a webwork, you found the expected value of x. You should now find its variance (assuming each person was born on any of 365 days equally likely, and independently from any other person).