1. Why is it so much more likely that some pair of people at aparty will have the same birthday, than that someone atthe party will have a birthday today?

Question : Reason = ? It is more likely that some pair of people at a party will have the same…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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8) In a class of 100 half the students are science majors and half are liberal art majors. A student who is a science major has a 0.9 probability of passing a given test whilst a student who is liberal art major has only a probability of 0.7. We pick 2 students at random without replacement and give them the test. What is the probability that both students pass the exam?
30. The chess clubs of two schools consists of, respectively, 8 and 9 players. four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that exactly one of Rebecca and Elise will be chosen to represent her school? Show the STEP-BY-STEP SOLUTION CLEARLY. SHOW EXPLAMATIONS IF NECESSARY.
1.) An archer can hit the bullseye of a target with an accuracy rate of 83%. Arrows hitting the bullseye are independent of each other. The archer is about to take 6 shots. Let X = the number of arrows (out of 6) that hit the bullseye. Describe the shape of the distribution, center, and spread of the distribution of X.
11. A car hiring company has 12 Tata sumos and 8 Qualis. If 5 of these cars go to workshop for repairs and Tata Sumo is as likely to be in for repair as a Qualis, what is the probability that (i) 3 of them are sumos and 2 are Qualis; (ii) at least three of them are sumos and (iii) all of them are of same make.
2. Use Bayes' theorem to solve the following: There are two bags. The first bag contains four mangoes and two apples; the second bag contains four mangoes and four apples. We also have a biased coin, which shows "Heads" with probability 0.6 and "Tails" with probability 0.4. If the coin shows "Heads". we pick a fruit at random from bag 1; otherwise we pick a fruit at random from bag 2. Your friend flips the coin (you cannot see the result), picks a fruit at random from the corresponding bag, and presents you a mango. What is the probability that the mango was picked from bag 2?
5. Suppose you live in an extremely unfortunate climate where it always rains on weekends (Saturday and Sunday). For that matter, there is always a chance of rain on a weekday (Monday-Friday) as well. If you have completely forgotten which day of week it is (so that it is equally likely to be any of the seven days), but you go outside and see that it's raining, what is the probability that it's the weekend?

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1. Why is it so much more likely that some pair of people at a party will have the same birthday, than that someone at the party will have a birthday today?