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?

Name: Solved: 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? - MathMaster
Brand: MathMaster
Rating: 4.9 (80 reviews)

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

113 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)

Question: What is the probability of obtaining exactly 3 "heads" in 5 coin tosses if the coin is fair?

What is the formula for finding the circumference of a circle with a radius of 5?

What is the median of the following set of data: 12, 18, 22, 15, 20, 14, 16, 19?

New questions in Mathematics

To calculate the probability that a player will receive the special card at least 2 times in 8 games, you can use the binomial distribution. The probability of receiving the special card in a single game is 1/4 (or 25%), and the probability of not receiving it is 3/4 (or 75%).

Let the vectors be u=(-1,0,2) , v=(0,2,-3) , w=(2,2,3) Calculate the following expressions a)<u,w> b) <2u- 5v,3w>

CASE 6-1: PREPARE A PRODUCTION PLAN: WHAT PROBLEMS ARRIVE? Midwest Plastics Company has conducted profit planning for several years. The president stated (with justification) that inventory control and planning had not been satisfactory, which was mainly due to poor planning of production and inventory budgets. Please analyze and provide recommendations, in detail, on the issue regarding the 20B profit plan, which is now being prepared. Their analysis and recommendations will be presented to the executive committee. Despite the seasonality factor, the sales department has been successful in developing a sales plan, on a monthly basis, for each year. The following sales data is available for 20B. 1. Sales plan summary for 20B: 2. Finished goods inventory, as of January 1, 20B, is 96,000 units. 3. Work-in-process inventory will remain constant. 4. Actual annual sales in 20A, including the estimate for December, were 350,000 units. 5. The average finished goods inventory during 20A was 70,000 units. IT IS REQUESTED. 1. Prepare the annual production budget, assuming that management policy is to budget ending finished goods inventory at a standard quantity, based on the ratio of historical sales of 20A to inventory turnover. 2. Prepare a schedule showing sales, production, and inventory levels for each month, assuming: 1) stable inventory, 2) stable production, and 3) recommended inventory-production levels. In developing your recommendations, assume that the following policies have been established: a) The president has set the policy that a maximum inventory of 85,000 units and a minimum inventory of 75,000 units should be used, except in abnormal circumstances. b) A stable level of production is definitely preferred, except that during the holiday season in July and August, production may be reduced by 25 percent. Likewise, a variation in production of 7.5 percent above and below the average level is acceptable. 3. What are the main problems faced by the company in production planning? Make your general recommendations.

two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?

Additionally, the boss asked Armando to determine how many toy sales branches he would have in the fifteenth year, knowing that the first year they started with two branches, by the second they already had 5 branches and, by the third year, they had 8 branches. From the above, determine the number of branches it will have for the fifteenth year.

The beta of a company is 1,41 and its cost of equity 18,95%. What is then the market risk premium if the risk free rate is 0,94%? (in %, 2 decimal places)

The mean life of a television set is 119 months with a standard deviation of 13 months. If a sample of 67 televisions is randomly selected, what is the probability that the sample mean would be less than 121 months? Round your answer to four decimal places