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April 18[edit]

Probability of having two birthdays fall on two consecutive days[edit]

What is the probability of having two birthdays fall on two consecutive days? To clarify what I am asking, I will use this example. A friend of mine had a baby on April 17. Years later, she had another baby on April 18. So, I wondered what is the probability of that occurring? I came up with 2/365, which equals 0.548% (slightly greater than one-half percent). But, this seems a bit too easy and simplistic; I feel as if I have missed something. For simplicity, I want to disregard February 29 and leap year dates. I just want to focus on the "regular" year of 365 days. Also, to be clear, if one child is born on April 17, the other child may be born on either April 16 or April 18, in order for the dates to be consecutive. So, I am asking about this, in general, throughout the year; I am not just asking for the specific dates of April 16, 17, 18. Thanks. Joseph A. Spadaro (talk) 16:05, 18 April 2018 (UTC)[reply]

Yes, you're correct. Sometimes, the maths is as easy as it seems. Iffy★Chat -- 16:35, 18 April 2018 (UTC)[reply]

Just a thought - Once the first baby is born, then there are 364 days to choose from (because if the second was born on the same date, it wouldn’t meet the requirement), so isn’t it 2/364? — Preceding unsigned comment added by 82.38.221.49 (talk) 20:26, 18 April 2018 (UTC)[reply]

There are 365 total days to choose from. In other words, the second baby can be born on any date from January 1 to December 31. Within any calendar year, two of those potential birth dates are "valid" (the two dates consecutive to the birth date of the first baby). Thus, 363 of those dates are "invalid". Out of those 363 "invalid" dates, indeed one of them is the actual corresponding (exact) birth date of the first baby. (Where "valid" means "fulfills the requirements of my posted question".) So, all possible birth dates (that is, 365) still need to be accounted for in the denominator. Again, leap years and February 29 are excluded in my premise. Joseph A. Spadaro (talk) 20:56, 18 April 2018 (UTC)[reply]

That would only be true if it were impossible for babies to be born on the same day but in different years. Iffy★Chat -- 20:34, 18 April 2018 (UTC)[reply]

If you're treating this as purely a mathematical problem and assuming that one day of the year is as likely as another, then with the simplifications indicated, 2/365 is correct. However, biology is not that simple. One obvious factor is that women are mostly likely to conceive a child within a few days of ovulation, which typically takes place about once a month, and as far as I know some form of the cycle continues during pregnancy. Since the duration of one successful pregnancy is typically about the same as as another, a woman whose personal cycle is close to exactly 1/12 of a year may have an increased probability on the original question. I have not searched for data to quantify or test this issue. --69.159.62.113 (talk) 01:56, 19 April 2018 (UTC)[reply]

Yes, I wanted to explore the question as a mathematical exercise. And, yes, there are other social and/or biological factors that can skew the data. You mentioned some. Another is the fact that some births can be "scheduled" (i.e., a Caesarean section, etc.). In some cases, one can choose (or not choose) to induce labor, etc. So, sometimes, individual actors (the mother, the doctor, etc.) can -- and, indeed, do -- directly influence and impact the date of the birth. But, I was simply looking at the mathematics behind my question. Thanks. Joseph A. Spadaro (talk) 03:11, 19 April 2018 (UTC)[reply]

My younger brother was born a day after like five of our relatives, including our grandmother. Grandmama was miffed Mom wouldn't induce labor the previous day. She also argued that I'd have trouble spelling my three-letter given name... Ian.thomson (talk) 03:16, 19 April 2018 (UTC)[reply]

Funny! Also, another social factor that will influence birth dates: I assume that some days (or seasons, or events, etc.) are more likely to attract the act of conception. For example, maybe more people are conceived in the summer versus the winter (or whatever). And, obviously, the deliberate act of conception will influence the date of birth. Also, another example: when men return home from war (on a grand scale), I believe I read that that impacts birth rates and so forth. Just some social factors to consider. But, again, my question was intended purely as a mathematical exercise. And a simplified one, at that (disregarding the mathematical complexity of leap days and leap years). Thanks. Joseph A. Spadaro (talk) 14:36, 19 April 2018 (UTC)[reply]

Thanks, all! Joseph A. Spadaro (talk) 22:40, 21 April 2018 (UTC)[reply]

Fractions and exponents in Microsoft Word[edit]

I was going to post my question in the Computer Reference Desk. But, I assumed that people here at the Math Reference Desk would be more familiar with this issue. When using Microsoft Word (Word 2016, to be exact), how can I type fractions that contain exponents? I know how to create fractions. I click Insert; then Equation; then Fraction. I select the "format" of the fraction that I want (Stacked Fraction). This places the cursor into the numerator and then, later, into the denominator. And I type in what I want for the numerator and for the denominator. However, I cannot seem to get exponents to work. When typing, say, "x squared", I type the "x" and then the "2" ... and I try to make the "2" become formatted as "superscript". But, I am not allowed to do so. Does anyone know how to accomplish variables that have exponents within fractions? Thanks. Joseph A. Spadaro (talk) 16:17, 18 April 2018 (UTC)[reply]

I am referring to something similar to the question posted directly above, where the editor asks about this equation:

{\frac {x^{2}}{3}}+1=y^{2}={\frac {z^{2}}{2}}-1

. Thanks. Joseph A. Spadaro (talk) 16:21, 18 April 2018 (UTC)[reply]

I never type fractions. I would write

3^{-1}x^{2}+1=y^{2}=2^{-1}z^{2}-1

. Bo Jacoby (talk) 19:40, 18 April 2018 (UTC).[reply]

Yes, but there are cases where fractions are necessary and unavoidable. Also, it seems silly (and overly complicated) to say "2 raised to the negative one power" as opposed to the fraction "1/2". No? Joseph A. Spadaro (talk) 20:53, 18 April 2018 (UTC)[reply]

Yes, I have often needed to type fractions in common format, and I've had to resort to small transparent text boxes. I'd be interested in a better method if there is one. Dbfirs 21:17, 18 April 2018 (UTC)[reply]

Whether

2^{-1}

is sillier than

1 \over 2

is a matter of taste. Root signs are unnecessary too:

{\sqrt {7}}=7^{2^{-1}}

. So are multiplication signs:

2\times 3=2^{1}3^{1}

. Bo Jacoby (talk) 06:01, 19 April 2018 (UTC).[reply]

Indeed, it is a matter of personal taste and preference. I was thinking of ordinary folks and lay persons, not necessarily people fluent in math. No lay person will understand the notation: "2 raised to the negative one power". Most barely understand fractions at all and the notation "1/2". Sad, but true. In any event, I had lay people in mind, not "math" people. Thanks. Joseph A. Spadaro (talk) 14:40, 19 April 2018 (UTC)[reply]

Suit yourself. I merely suggested a solution to your problem. There is no such thing as ordinary folks and lay persons. We all have to learn, and unnecessary complications should be avoided. Fraction bars, root signs and multiplication signs are unnecessary complications. Bo Jacoby (talk) 18:00, 19 April 2018 (UTC).[reply]

Unnecessary, but useful for legibility. Expressing things using as few different constructs as possible may be useful if you're trying to prove something related to how things are expressed, but there's a reason why fraction bars and root signs are commonly used. --69.159.62.113 (talk) 22:53, 19 April 2018 (UTC)[reply]

The reason why fraction bars and root signs are commonly used is probably purely historical. Bo Jacoby (talk) 07:01, 20 April 2018 (UTC).[reply]

Word v4 (1988) had a nice easy syntax for such things, sigh. —Tamfang (talk) 08:16, 19 April 2018 (UTC)[reply]

I did find a helpful feature in Word, after all. I click Insert; then Equation; then Fraction. As stated above. Then, I can click "Scripts". This allows me to place exponents and superscripts and subscripts within the fraction's numerator and/or denominator. Thanks. Joseph A. Spadaro (talk) 22:44, 21 April 2018 (UTC)[reply]

Thanks, all! Joseph A. Spadaro (talk) 22:41, 21 April 2018 (UTC)[reply]