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If you have 10 people in a room, what are the odds that two of them have the same birthday

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Calculating the Odds of Two People Sharing the Same Birthday in a Room of 10

The question "If you have 10 people in a room, what are the odds that two of them have the same birthday?" explores the probability of two individuals sharing the same birth date within a group of ten people. By understanding the concept of probability and applying a straightforward calculation, we can determine the likelihood of this occurrence.

Benefits of Understanding the Odds:

  1. Insight into Probability:

    Understanding the odds of two people sharing the same birthday in a room of 10 provides valuable knowledge about probability. This skill can be applied in various scenarios, such as risk assessment, decision-making, and predictions.

  2. Party Games and Icebreakers:

    Knowing the odds of shared birthdays can add an element of fun to social gatherings. It allows you to create games or trivia questions centered around birthdays, enhancing the entertainment value of your events.

  3. Mathematical Curiosity:

    Exploring the probability of shared birthdays sparks mathematical curiosity and encourages critical thinking. It offers an opportunity to delve into concepts like permutations, combinations, and the birthday paradox.

Calculating the Odds:

To determine the odds of two people having the same birthday in a group of 10, we can use a simplified approach:

The chance of: two people sharing a birthday would be 1 - (364/365), or 0.3%, or 1 in 370. three people sharing a birthday would be 1 - ((364/365)(363/365)), or 0.8%, or 1 in 122.

What is the rarest birthday?

The least common birthday is leap day, or February 29. But because the day only occurs once every four years, it's obvious it would yield the least amount of birthdays. The rarest birthday of the 365 annual calendar days is Christmas Day, Dec. 25.

What are the odds of dating two people with the same birthday?

If you have only 2 girlfriends then the chances they share the same birthday (the same day and the same month but not necessarily the same year) is 1/365 = approximately 0.27%.

Is the birthday paradox true?

The birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50%. The birthday paradox is a veridical paradox: it seems wrong at first glance but is, in fact, true.

What is the golden birthday mean?

Your golden birthday is the year you turn the same age as your birthday – for example, turning 25 on the 25th, or 31 on the 31st. If you've ever wondered where the tradition comes from, you're not alone. Joan Bramsch, a midwestern author, started celebrating her five children's golden birthdays in the 1950s.

How many people in a room to have the same birthday?

In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. The birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50%.

What are the odds of 30 people in a room having the same birthday?

The probability of sharing a birthday = 1 − 0.294... = 0.706... Or a 70.6% chance, which is likely! So the probability for 30 people is about 70%.

Frequently Asked Questions

Can 23 people in a room share the same birthday?

23 people. In a room of just 23 people there's a 50-50 chance of at least two people having the same birthday. In a room of 75 there's a 99.9% chance of at least two people matching. Put down the calculator and pitchfork, I don't speak heresy. The birthday paradox is strange, counter-intuitive, and completely true.

What is the probability that 10 people have different birthdays?

If ten people are randomly selected, the probability that all have different birthdays is 0.883. The chances for the second person to be born on the same day as the first person will reduce by one of the first people having a birthday on any of the 365 days, and so on.

How many people do you need in a room to share a birthday?

23 people What is the Birthday Paradox? Wherever you are, if there are 23 people in the room with you, there is a 50/50 chance that two people have the same birthday. And that is the "Birthday Paradox”.

Why is it that in a room of 23 people there's a 50% chance two people have the same birthday?

Thus, an assemblage of 23 people involves 253 comparison combinations, or 253 chances for two birthdays to match. This graph shows the probability that there is at least one pair of people with the same birthday among a certain number of people. Here's another exponential growth problem similar to the birthday paradox.

What is the probability that two of 23 people have the same birthday?

About a 50 percent chance The birthday paradox, also known as the birthday problem, states that in a random group of 23 people, there is about a 50 percent chance that two people have the same birthday.

FAQ

How many people in a group to have two with the same birthday?
23 people. In a room of just 23 people there's a 50-50 chance of at least two people having the same birthday. In a room of 75 there's a 99.9% chance of at least two people matching. Put down the calculator and pitchfork, I don't speak heresy. The birthday paradox is strange, counter-intuitive, and completely true.
What are the odds you have the same birthday?
One person has a 1/365 chance of meeting someone with the same birthday. Two people have a 1/183 chance of meeting someone with the same birthday. But! Those two people might also have the same birthday, right, so you have to add odds of 1/365 for that.
What is the probability that no two share the same birthday if we have 25 students in class?
0.431 For all birthdays to be unique, the number of favorable options decreases by one at every successive individual. However, the total number of options remains the same. Therefore, the probability that out of 25 selected people, all will have unique birthdays is 0.431.
What are the odds of 2 people having the same birthday?
The chance of: two people sharing a birthday would be 1 - (364/365), or 0.3%, or 1 in 370.

If you have 10 people in a room, what are the odds that two of them have the same birthday

What is the probability that two friends have same birthday? What's the chance that two people share the same birthday? The first person can be born on any day of the year, this means that the probability is 365/365 = 1. The second person has to be born on the same day as the first and there is a 1/365 chance of that happening.
What is the probability that 25 randomly selected students at least two share the same birthday? Approximately 0.568 The probability that exactly 2 people have the same birthday in a group of 25 people is approximately 0.568, or 56.8%. This is calculated using the formula for the probability of at least two people sharing a birthday, which is 1 - (365!/((365-n)!*
What is the probability that 2 out of 25 people have the same birthday? Answer: The Probability that of 25 Randomly Selected Students, at Least Two, Share the same Birthday is 0.5687.
What are the odds to find someone with the same birthday? The odds are 1/366, or 0.0027%! And those aren't very good odds. That's why when you meet someone who has the same birthday as you, it always seems like a neat coincidence.
  • What is the probability of 30 people in a room having the same birthday?
    • The probability of sharing a birthday = 1 − 0.294... = 0.706... Or a 70.6% chance, which is likely! So the probability for 30 people is about 70%.
  • Can 75 people in a room share birthday?
    • With 75 people in a room, there is a 99% chance that at least two people will have the same birthday.
  • What is the probability of 2 people not sharing the same birthday?
    • The probability that a person does not have the same birthday as another person is 364 divided by 365 because there are 364 days that are not a person's birthday. This means that any two people have a 364/365, or 99.726027 percent, chance of not matching birthdays.
  • What is the rarest birthday date?
    • What are the rarest birthdays? Surprisingly, none is in February. They cluster around holidays. December 25, January 1, December 24, July 4, January 2, December 26, November 27, November 23, November 25 and October 31st.