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Steve
Jordan
ProfessorThe simplistic answer is 1/7 but things are quite that simple. Births are not evenly distributed over days of the week.
Statistical studies of days of birth across the world have shown that the Birth Rate is lower over weekends than during weekdays - Fridays to Sundays, depending on where in the world you live. This is particularly so for induced births or ones which require surgical intervention. In such cases maternity services would wish to ensure that they were appropriately staffed: not surprisingly, medical staff wish to spend time with their families over weekends. So the probability of a Monday birth is greater than 1/7.
In the UK, between 1979 and 2014, the pattern was, Sunday (lowest), Saturday, Monday, Tuesday, Wednesday, Thursday and Friday highest). Christmas Day, Boxing Day and public holidays were excluded for this ranking,
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What is the probability of at least one birthday match among a group of 41 people?
The probability of at least 1 match is equivalent to 1 minus the probability of there being no matches. The first person's birthday can fall on any day without a match, so the probability of no matches in a group of 1 is 365/365 = 1. The second person's birthday must also fall on a free day, the probability of which is 364/365 The probability of the third person also falling on a free day is 363/365, which we must multiply by the probability of the second person's birthday being free as this must also happen. So for a group of 3 the probability of no clashes is (363*364)/(365*365). Continuing this way, the probability of no matches in a group of 41 is (365*364*363*...326*325)/36541 This can also be written 365!/(324!*36541) Which comes to 0.09685... Therefore the probability of at least one match is 1 - 0.09685 = 0.9032 So the probability of at least one match is roughly 90%
What is the probability of being born on a Monday?
1 out of 7 I think so!
If 15 strangers are all in a room what is the probability of them all having the same birthday?
To determine the probability of 15 random people all having the same birthday, consider each person one at a time. (This is for the non leap-year case.)The probability of any person having any birthday is 365 in 365, or 1.The probability of any other person having that same birthday is 1 in 365, or 0.00274.The probability, then, of 15 random people having the same birthday is the product of these probabilities, or 0.0027414 times 1, or 1.34x10-36.Note: This answer assumes also that the distribution of birthdays for a large group of people in uniformly random over the 365 days of the year. That is probably not actually true. There are several non-random points of conception, some of which are spring, Valentine's day, and Christmas, depending of culture and religion. That makes the point of birth, nine months later, also be non-uniform, so that can skew the results.
What is the probability that no two people have the same birthday out of 55?
Leaving aside leap years, the probability is 0.0137
What is the probability of 2 or more people in a a group of about 30 having the same birthday?
The probability with 30 people is 0.7063 approx.
