TASK 3 Work out how many people you need to meet before it is more likely.LS I t
ID: 3370883 • Letter: T
Question
TASK 3 Work out how many people you need to meet before it is more likely.LS I than not that you come across someone whose birthday is on the same date as yours. What assumption are you making? (Assume a year is 365 days and the birthday is not on 29 February). a) 1 72 b) The probability that a roll of wallpaper has a defect is i. Given that the probability of a defect is very small, choose any L41 four values of n and work out the probability of a defect not occurring in a single roll of wallpaper. i. An inspector examines n rolls of wallpaper. Work out the probability of a defect not occurring in any of them, for each of your values of n. What do you notice about your four answers? 5 1 i Investigate further. SEE NEXT PAGEExplanation / Answer
How many you need to meet before it is more likely than not that you come across someone whose birthday is on the same date as YOURS?
Assume a year is 365 days
Since there is a restriction on which two people will share a birthday, that is you are sharing a birthday with someone.You need 365/2 = 182.5 so the closest whole number is 183.
Thus you need 183 people who have need to meet before it is more likely than not that you come across someone whose birthday is on the same date as YOURS
Had it been that there was no restriction on who is sharing the birthday, you would need 23 people in a room so that any two of them share birthday may or may not be with you.
With just two people, the probability that they have different birthdays is 364/365, or about .997.
If a third person joins them, the probability that this new person has a different birthday from those two (i.e., the probability that all three will have different birthdays) is (364/365) x (363/365), about .992.
With a fourth person, the probability that all four have different birthdays is (364/365) x (363/365) x (362/365), which comes out at around .983. And so on.
The answers to these multiplications get steadily smaller. When a twenty-third person enters the room, the final fraction that you multiply by is 343/365, and the answer you get drops below .5 for the first time, being approximately .493. This is the probability that all 23 people have a different birthday. So, the probability that at least two people share a birthday is 1 - .493 = .507, just greater than 1/2.
Please post next part as a separate question as they are not related. Thank you.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.