1. A newspaper article about a family in which a woman, her daughter and her gra
ID: 3070144 • Letter: 1
Question
1. A newspaper article about a family in which a woman, her daughter and her grandson have the same birthday claimed the chance of this is "one in nearly 49 mllion, according teo statisticians"1 (that is, 3igring leap day) 3653 (a) Why is this wrong (and no thoughtful statistician would have stated it), and what is the correct probability? Hit ho many birthdays could they share? (b) We often have a tendency to focus on the probability of a specific coincidence rather than on the fact that there is some coincidence. Consider instead the following situation. Imagine that two individuals have two children, one who produces 1 grandchildren and the other who produces 2 grandhild What is the chance that there is a progression parent child grandchild sharing birthdays? To simplify things, you can assume the possibility of this happening more than one way is relatively negligible, including the possibility of multiple births (such as twins) ignore multiple scenarios in the same family.) a birthday. What is the chance they are in a parent child grandchild progression? (c) What is the chance that three people in the family of ten share a birthday? (Again, (d) Continue to assume as in parts (b) and (c), and suppose three people in the family share (e) Obviously families come in different sizes. But suppose there is approximately a 10 chance of a grandparent parent child sequence sharing a birthday in a family and fam- ilies are independent. What is the chance that this occurs in at least one family for a city of 30,000 families? How do you view the ”coincidence" of the news article now?Explanation / Answer
For any given 3 people for which we can reasonably expect that their birthdays are relatively effectively random, it will be about 1 in (365*365). However, you have not told us how many different subsets of 3 can be selected from you family. To a first approximation, you can just multiply by that number.
There is no sample size given in the question. Three people share their bday out of how many people??
Lets say if there are 87 people, the probability of at least three people sharing a birthday is very close to 0.50 (making the standard assumption of an uniform distribution over 365days).
On the face of it, for three particular people independently to have the same birthday, the probability is about 1/(365)(365) (rather more because they are not independent if families are planned).
What's the probability that, in a family of ten, exactly three people have the same birthday?
For a family of ten: (365C8 * 10! / 3!) / 365^10 =
((7232294429652435 * 3628800)/6)/4.1969002243198805e+25)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.