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The number of those should be 10! At least one of those must be wrong. The other reason I think your approach is flawed is that it will give a positive probability of a bday every day even if you have fewer friends than there are days in the year.
But, as you noted already, that can't be true. Unfortunately, I don't know how to correctly calculate the chances of having an un-bday in a normal year with any arbitrary number of friends.
I suspect the problem in your approach lies in treating probabilities as if they were independent when they actually aren't, but I'm not sure. No, Ethan's right, but there's a simpler illustration. Using a die for the example: Yes, I agree that gives the correct odds of no one having a birthday on any single day.
It's the next part that I think is wrong - calculating the odds that no one has a birthday on at least one day in the whole year.
Again, if you use Ethan's approach with only friends, you get a non-zero chance of there being a birthday on every day of the year.
Yet that's clearly impossible when there are fewer friends than there are days. So I'm still pretty convinced that something's wrong, even if I can't give what I think would be the correct calculation. I'm also not sure the calculation on the probabilities of there being at least one birthday-free day is correct.
If I did the math right i.
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I also wrote a little program to randomly assign birthdays to different people, and then check if there is at least one day without a birthday.
Doing this 10, times, 7, Even taking into account the randomness of the process, this is far enough from the number above Rick, I also wrote a quick code, and I think you are answering a different question than Ethan is. Your question is whether any day in the year exists without birthdays. It would seem that those two probabilities are related, but significantly different.
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What if we wanted to know what the odds are of having at least one day in the year where no one has a birthday? Steven, as qetzal points out, the post asks two related questions, the first is the probability of a person having a birthday today, and then generalizes the question to "What if we wanted to know what the odds are of having at least one day in the year where no one has a birthday?
It's the answer to the second that seems to be incorrect.
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I think the problem may be that the approach used assumes statistical independence of the probability of the number of birthdays on each day, when they are not actually independent. For instance, if we have 2, friends and today has no birthdays, then all the 2, birthdays need to be distributed over rather than days, while if today has 10 birthdays, then the other days will have only birthdays distributed over them.
Thus the number of birthdays today affects the probability of birthdays falling on every other day. Suppose after X birthdays have been randomly chosen, the probability of their being n days without birthdays is p[n].
Now, if another birthdays is added, then if they birthday falls on a day that another birthday already falls on, then the number of birthday-free days does not change. I wrote a program which iterates through this for all possibilities of free days before any birthdays have been added to 0 free days.
Within the limits of precision of the floating point numbers, I get the following:. There is indeed a problem with the "at least one person has a birthday every single day" approach. Ethan's approach would work in a slightly different situation: If we took a random sample then checked for the first of Jan, then took a second sample and checked for the second of Jan, etc.
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However this is different from the question posed. The problem is that within a single sample i. The problem with this method can be shown with the example of a year with 2 days and 2 people.
Can someone please calculate this compound probability question for me? Whatis the probabiiity of five our 25 people having birthdays in November?
Did you seriously just use someone's creepy foot fetish deviant-art as a visual aid here? Don't you realize the person who drew it did so for masturbation purposes? The no-birthday paradox facebook twitter reddit linkedin email print. By esiegel on January 31, More like this Non-Existent Birthdays. Just in case you missed the date on the headline, it is midnight, after February 28th, and just before March 1st.
If there were a day in between yesterday and tomorrow, it would be my birthday. Next year, there will be one. This isn't next year. This year, I lack a birthday. Y our Birthday Number is like a gift that you have to give — both to yourself and to the world. This number indicates a certain aspect of yourself and your personality that might be in sync with your other numbers or it could possibly explain why you feel you walk a delicate balance with the way you see yourself, your desires and your actions.
Some numerologists place a lot of weight on the date of birth - so much so that they see the Birthday number as taking precedence over the Life Path number in importance. For instance, Lloyd Strayhorn author of Numbers and You asserts that: Your birth date, on the other hand, sees you as the 'pupil,' and indicates what you're here to study, learn and master.
The more I work with people and their numerology charts, the more I see this number as an indicator of where you might feel the most comfortable - like that old comfy robe that you just can't bear to part with.
And yet you're being called upon to take the gifts you bring with the Birthday number and carry them forward into your Life Path purpose.
The energies you contain with the Birthday number are at their highest and best use when you're integrating them with your Life Path strengths and using it to enrich your Life Path purpose.
You have a creative mind, great business instincts and with the right training and initiative, can achieve great things in the material world. You have a broad vision and are able to get creative ideas up and running. Prone to laziness and procrastination, you can resort to angry outbursts and frustration.
You prefer to blame others for your ineffectiveness. Instead of working with others, you tend to plow through with blinders on without taking others into consideration.
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You force issues rather than working with a balanced perspective. You sit on the sidelines and never risk taking the lead. Your talents reside in your harmonizing abilities, personal relations, and sensitivity to others. You bask in beauty, attention, and can often be gifted artistically and musically.
You gravitate toward safety, security, and love. You can feel like a victim and suffer from depression and a deep lack of confidence. Your presence is galvanizing, yet your highest and best use is to inspire others through your example.
You experience nervous tension and an inability to shield yourself from the onslaught of negative emotional energy from those around you.
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Your mind works intuitively - understand that your over-all sensitivity is your blessing and your curse. You have amazing creative talent and are an artist at least at heart. In order to feel satisfied in your life, you need to engage in some sort of creative outlet or hobby.
Moody with roller-coaster emotional ups-and-downs, you can find yourself in the depths of despair and back again like a yo-yo. You find that your glass is half empty and life feels emotionally debilitating and often hopeless. Passive-aggression or sarcasm becomes your emotional weapon of choice. You tend to dig in, hover, and wait — cutting you off from opening yourself to other solutions or creative ideas.
Since you struggle with inflexibility, you often experience repression, frustration, and a feeling of insurmountable limitation.
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You can teeter toward blunt and tactless communication; yet not understand that other people are attempting to communicate on a more creative or emotional realm, which sometimes feels foreign to you. Your potential is boundless as a leader, organizer, or founder of a business or institution.
You can be fearful of your ambitions and feel undeserving. You have a quick mind and love shaking it up and exploring the world. You attract people from all walks of life and love to experience the exotic.
Impatient, impulsive, and excessive, you lean toward over-indulgence and irresponsibility. You are the drama Queen or King, demanding constant activity and stimulation. You are easily bored, distracted, and restless — with a mantra of: The key is to discipline your energies, contain your focus, and develop light routine and orderliness in your life.
You can also experience the opposite — which is the ultimate Fear Factor. You can feel too fearful about the world, paranoid, and unable to focus, follow-through, and be productive.
Family-oriented, responsible, and nurturing are your trademarks. You often have a knack for bringing out the best in those around you. You often are a natural artist or musician and can also gravitate toward the healing arts.
Your focus is on relationships and helping others. Children and animals usually are naturally attracted to you and your energy.