Wikipedia:Reference desk/Archives/Mathematics/2017 August 10

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August 10

Death day probability

What is the probability that a person's death day occurs later in the calendar year than their birth day? -- Jack of Oz ^{[pleasantries]} 20:34, 10 August 2017 (UTC)

About the same as the chance of their birth day being after their death day in the calendar year I'd have thought. Dmcq (talk) 20:59, 10 August 2017 (UTC)

How about solving an easier problem first. What is the probability the "death day of the week" occurs later than the "birth day of the week". For example, if a person is born on Tuesday what if the probability that the death day is wed, thu, fri or sat ?? 96.66.16.169 (talk) 22:34, 10 August 2017 (UTC)

Birth day is day number b of the year, and death day is day number d of the year. Pr(b=d) = 1/365. Pr(b≠d) = 364/365. Pr(b<d) = Pr(b>d) = 182/365. Bo Jacoby (talk) 22:51, 10 August 2017 (UTC).

This assumes the days are random and leap days are ignored. Several real World factors will influence the actual probability but I don't know how and it will depend on the location. Some of the factors are seasonal variations in birth and death rates, infant mortality increasing deaths shortly after birth, and birthday effect. PrimeHunter (talk) 23:33, 10 August 2017 (UTC)

OK, so in rough terms it's 50 percent. Thanks for that.

Now, I wonder if the following is a different question or not:

• For a given birth day, what is the probability that a person's death day occurs later in the calendar year than their birth day?

Obviously, for a 1 January birth day the probability is 364/365, and for a 31 December birth day it's exactly zero because there is no later date than 31 December. For any other date it's somewhere in-between. But if the date isn't specified, the problem seems to resolve to the original question. True? -- Jack of Oz ^{[pleasantries]} 02:04, 12 August 2017 (UTC)

If we're talking about people in general with an even chance of being born or dying throughout the year then yes. If we're talking about people who were born in March then no. And the actual statistics show more people are born in July to October and die in December to March and there may be statistics on the correlation between birth and death date as well. Dmcq (talk) 17:39, 12 August 2017 (UTC)

Q: For a given birth day, what is the probability that a person's death day occurs later in the calendar year than their birth day?

A: Again, birth day is day number b of the year, and death day is day number d of the year. Assuming that b is known, then the conditional probabilities are Pr(b=d | b) = 1/365, Pr(b≠d | b) = 364/365, Pr(b<d | b) = (365-b)/365, and Pr(b>d | b) = (b-1)/365. Remenber to include an improved answer when criticizing. Bo Jacoby (talk) 22:51, 10 August 2017 (UTC).

Who criticised? -- Jack of Oz ^{[pleasantries]} 20:42, 12 August 2017 (UTC)

You want criticism eh? Well I'll give you criticism ;) Even assuming the birth dates aand death dates are evenly spread throughout the year that does not mean there is a near half chance the death date is after the birth date. For instance if Lastday was when we died at a certain age like in a version of Logan's Run then the death date would be the same as the birth date so noone would have their death date after their birth date. Or if you think the millenium should have been celebrated in 1999, or is that 2001 compared to 2000 perhaps I got that wrong, then only people born on the first day of the year would have their death date after their birth date. Dmcq (talk) 10:24, 13 August 2017 (UTC)

And what is your improved answer to the question? Bo Jacoby (talk) 12:31, 13 August 2017 (UTC).

We'd need to know more about the question to give a better answer, a lot of assumptions have been made. With what is in the question mathematically about the best we can say is that for a population of people the probability of their death day being after their birth day is the number of those for whom the death day is after the birth day divided by the total number. And specifying the population can be difficult - for instance at a particular time the people with a long lifetime are better represented than those with a short lifetime. Dmcq (talk) 13:07, 13 August 2017 (UTC)

As the answer reflects what we do know about the question, we can give no better answer. Nor do we need a better answer. For any purpose the answer given is sufficiently precise. Bo Jacoby (talk) 11:00, 14 August 2017 (UTC).