MathMaster logo

MathMaster

  1. Home
  2. general
  3. there are 20 people in a room assume each person s birthday is equally likely to be any of the 365 days of the year a what
Question

There are 20 people in a room. Assume each person’s birthday is equally likely to be any of the 365 days of the year. (a) What is the probability that no one in the room share the same birthday? [5] (b) What is the probability that exactly two people have the same birthday? [5] (c) What is the probability that two or more people have the same birthday?

80

likes
398 views

Answer to a math question There are 20 people in a room. Assume each person’s birthday is equally likely to be any of the 365 days of the year. (a) What is the probability that no one in the room share the same birthday? [5] (b) What is the probability that exactly two people have the same birthday? [5] (c) What is the probability that two or more people have the same birthday?

Expert avatar
Dexter
4.7
114 Answers
已知信息： - 一个房间里有20个人。 - 每个人的生日都有可能出现在一年 365 天中的任何一天。 （a）房间里没有人同天生日的概率： 第一个人的生日可以是 365 天内的任何一天。 对于第二个人，剩余 364 天（共 365 天）可供选择，因此他们的生日与第一个人的生日不同。 对于第三个人，剩余 363 天（共 365 天）可供选择，因此他们的生日与前两个人不同。 继续这个过程，没有人同天生日的概率是： 概率 = (365/365) × (364/365) × (363/365) × ... × (346/365) 概率 = \frac{\left(365\cdot364\cdot363\ldots..346\right)}{365^{20}} （b）恰好两个人有同一天生日的概率： 步骤1：计算从20个人中选择2个人的方法数。 选择 2 个人的方式数 = 20 的组合取 2 = (20 × 19) / (2 × 1) = 190 第 2 步：计算选择两个人共享生日的特定日子的方法数。 选择特定日期的方式数 = 365 步骤3：计算将剩余18个人分配到另外364天的方法数。 剩余18人的分配方式数=365p18/365^18 步骤 4：将步骤 1、2 和 3 的乘积除以可能结果的总数来计算概率。 可能结果总数 = 365^20 概率 = (190 × 365 × 365p18 / (365^18)) / (365^20) （c）两个或两个以上的人有相同生日的概率： 两人或两人以上生日相同的概率 = 1 - 无人生日相同的概率 概率 = 1 - (365p20 / (365^20))

Frequently asked questions (FAQs)
Math question: Find the 4th order derivative of f(x) = 3x^5 + 2x^3 - 7x^2 - 4x + 1.
+
Question: What is the volume of a right circular cylinder with radius r and height h?
+
What is the derivative of f(g(x)) when f(x) = x^2 and g(x) = sin(x)?
+
New questions in Mathematics
Two fire lookouts are 12.5 km apart on a north-south line. The northern fire lookout sights a fire 20° south of East at the same time as the southern fire lookout spots it at 60° East of North. How far is the fire from the Southern lookout? Round your answer to the nearest tenth of a kilometer
Hey👋🏻 Tap "Create New Task" to send your math problem. One of our experts will start working on it right away!
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
For a temperature range between 177 degrees Celsius to 213 degrees Celsius, what is the temperature range in degrees Fahrenheit.
An integer is taken at random from the first 40 positive integers. What is the probability that the integer is divisible by 5 or 6?
The equation of the circle that passes through (5,3) and is tangent to the abscissa axis at x=2 is a.(x-2)^2 (y 3)^2 = 9 b.(x-2)^2 (y-3)^2 = 9 c.(x-2)^2 (y-3)^2 = 4 d.(x-2)^2 (y 1)^2 = 4 e.(x-2)^2 (y-1)^2 = 4
4x/2+5x-3/6=7/8-1/4-x
Primes are numbers divisible only by 1 and themselves; There are infinitely many prime numbers and the first ones are 2, 3, 5, 7, 11, 13, 17, 19, 23, .... Consider a 12-sided die, with the faces numbered from 1 to 12. Out of 4 rolls, the probability that only the first three numbers are primes is:
Three squares have a total area of 35.25 𝑐𝑚2 . The larger square has twice the side-length of the middle-sized square. The smaller square has its side length exactly 0.5 cm smaller than the middle-sixed square. Find the side lengths of each of the three squares.
What’s the slope of a tangent line at x=1 for f(x)=x2. We can find the slopes of a sequence of secant lines that get closer and closer to the tangent line. What we are working towards is the process of finding a “limit” which is a foundational topic of calculus.
3 A tree is planted when it is 1.2 m tall. Every year its growth is 3/8 of its previous year's height. Find how tall the tree will grow.
Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4336 patients treated with the​ drug, 194 developed the adverse reaction of nausea. Construct a ​99% confidence interval for the proportion of adverse reactions.
392929-9
For what values of m is point P (m, 1 - 2m) in the 2⁰ quadrant?
In a physics degree course, there is an average dropout of 17 students in the first semester. What is the probability that the number of dropouts in the first semester in a randomly selected year has between 13 and 16 students?
36 cars of the same model that were sold in a dealership, and the number of days that each one remained in the dealership yard before being sold is determined. The sample average is 9.75 days, with a sample standard deviation of 2, 39 days. Construct a 95% confidence interval for the population mean number of days that a car remains on the dealership's forecourt
17. A loan for $104259 is taken out for 10 years with an annual interest rate of 9.4%, compounded quarterly. What quarterly payment is required to pay the loan off in 10 years? Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
Given the word WEIRD, determine a four-letter offspring that can be formed with the letters of the word written above
The average weekly earnings in the leisure and hospitality industry group for a re‐ cent year was $273. A random sample of 40 workers showed weekly average ear‐ nings of $285 with the population standard deviation equal to 58. At the 0.05 level of significance can it be concluded that the mean differs from $273? Find a 95% con‐ fidence interval for the weekly earnings and show that it supports the results of the hypothesis test.
-Please answer to the following questions: What is the price elasticity of demand? Can you explain it in your own words? What is the price elasticity of supply? Can you explain it in your own words? What is the relationship between price elasticity and position on the demand curve? For example, as you move up the demand curve to higher prices and lower quantities, what happens to the measured elasticity? How would you explain that? B-Assume that the supply of low-skilled workers is fairly elastic, but the employers’ demand for such workers is fairly inelastic. If the policy goal is to expand employment for low-skilled workers, is it better to focus on policy tools to shift the supply of unskilled labor or on tools to shift the demand for unskilled labor? What if the policy goal is to raise wages for this group? Explain your answers with supply and demand diagrams. Make sure to properly cite and reference your academic or peer-reviewed sources (minimum 2).

You might be interested in