IF Andrea was born on Monday, what is the probability that after 23 years, her birthday is still Monday?

Question

IF Andrea was born on Monday, what is the probability that after 23 years, her birthday is still Monday?

We are talking of probabilities here...
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please consider all types of years(leap years and the years 100, 200, 300, etc.) and all types of dates(whether born before or after feb.29)
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Answer 1

The probability is 24.25%, or 0.2425.

I thought about your question for a while, and realized it matters whether Andrea could have been born before 1900. Since Andrea was not a common name prior to the twentieth century, I thought it safe to assume she was born sometime after 1900.

But then I re-read your question, and realized you want all years considered. I'll still rule out BCE dates since there was no year zero.

Before thinking about leap years, there are 52 weeks and one day in a year. So in 23 years, these extra 23 days cover 3 weeks and two days. Without leap years, Andrea's 23rd birthday would be on a Wednesday.

Now we begin to think about leap years. Ignoring, for a moment, the century years, Andrea will have experienced a Leap Year Day (LYD) before her 4th, 8th, 12th, 16th, and 20th birthdays. And if those are the LYDs she experiences, then there's a 100% chance that her 23rd birthday will be on a Monday.

Still ignoring the century years, the question now is whether Andrea experienced a LYD between her 20th and 23rd birthdays. And that probability would be three-fourths. So if that's all there is to the problem, we'd say there's a 25% chance Andrea's 23rd birthday is on a Monday.

Now we consider the century years, and see that there's a simple adjustment to finish off this problem. Until now, we'd assumed one LYD every four years, and that "1 in 4" gave us our 25% answer so far.

But in fact there are only 97 LYDs every 400 years. So instead of "1 in 4" or "100 in 400", we'll use "97 in 400", so the probability that Andrea's 23rd birthday is on a Monday is 24.25% (answer).

I'd add two comments. First, it doesn't matter whether Andrea was born before or after Feb. 29th. The way I set it up, it only depends on how many LYDs Andrea experienced in the 23 years.

The second comment is that it would be more complicated if Andrea were born on a LYD. About 1 in 1500 people are (1 in 1461, times 0.97). Worst case would be if Andrea were born on a LYD in the 19th century. Suppose she was born on 29 February 1896. (Some people were.) Then her first birthday was on 29 February 1904, by which time she'd have been eight years old, and her 23rd birthday (if my arithmetic holds up) was on 29 February 1992.

But consideration of that wrinkle is beyond me, at least right now. I'll stick with 24.25%.

Answer 2

It's 25%, or a whisker less than it. If there were no leap years, her birthday would be Monday every seven years, and Wednesday after 23 years. To bring it to Monday again she needs five extra Feb 29ths. Depending on the year she was born, in the next 23 there are 5 of those 25% of the time and 6 of them 75% of the time.

There was no Feb 29 in 1800 or 1900, so if her 23 years included that moment, there would instead have been 4 occurrences of Feb 29 25% of the time and 5 of them 75% of the time. I don't know the probability that this might apply, so I don't know how much to adjust the 25% answer by.

Answer 3

1 in 14

Answer 4

It would be a 1 out of 7 chance since there are 7 days in a week.

Answer 5

you ask the wrong question... you can either guess, in which case the chance is 1/7.... or you can go and calculate, which is possible, but probability does not come into it.

Answer 6

50%