Finding the probability of repeats in finite sequences
1. What is the probability that out of 3 people, 2 were born in the same month.
2. What is the probability that a seven digit phone number has 1 or more repeats.
3. What is the probability that given 5 letters selected randomly from the alphabet, none is repeated?
4. What is the probability 2 of more randomly selected senators have the same birthday (100 senators).
The solution comprises 1 1/2 pages written in Word with equations in Mathtype. The first 3 questions are answered using basic probability and logic. The final question, known as the Birthday Problem, is more subtle. Whilst logic and basic probability do give an exact expression for the answer, calculators are not able to calculate this value (the numbers get too big) and more complicated techniques have to be employed (approximating first as a Binomial then as a Poisson distribution, or writing an iterative computer program) to obtain a numerical solution.
Full explanation is given for each part of the solution.
- Plain text response
- Attached file(s):
- 168823 Solution.doc
- Your Information is Secure
- Best Online Academic Help Service
- Students find real academic Success
- Probability and Birthdays - From a set of n randomly chosen people, let Eij be the event that persons i and j have the same birthday. Assume that each person is equally likely to have any of the 365 days of the year as his or he ...
- Determining the probability from a given situation. - What is the probability that at least 2 of the 435 members of the House of Representatives have the same birthday?
- Probability: Birthdays on the Same Day - Determine the number of people needed to ensure that the probability at least two of them have the same day of the year as their birthday is at least 70 percent, at least 80 percent, at 90 percent, 95 ...
- Probability - 6. If there are 12 strangers in a room, what is the probability that no two of them celebrate their birthday in the same month?
- Algebra Word Problems - When asked about her birthday, a young woman gives the following information: "The day after tomorrow, I turn 22, but I was still 19 on New Year's Day last year." What is her birthday?
