22. In 1710, J. Arbuthnot observed that male births had exceeded female births in London for 82successive years. Arguing that the two sexes are equally likely, and 2-82 is very small, he attributedthis run of masculinity to Divine Providence. Let us assume that each birth results in a girl withprobability p = 0.485, and that the outcomes of different confinements are independent of each other.Ignoring the possibility of twins (and so on), show that the probability that girls outnumber boys in 2nlive births is no greater than (2) p"q"{q/(q- p)}, where q = 1 - p. Suppose that 20,000 childrenare born in each of 82 successive years. Show that the probability that boys outnumber girls everyyear is at least 0.99. You may need Stirling's formula.

Answered: Image /qna-images/answer/b3d1a31c-f80b-42f0-a9af-405b5788d66b.jpg

Answered: 22. In 1710, J. Arbuthnot observed that…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A bowl with Christmas candy contains two types: 7 different individually wrapped cookies and 14 different fun-size candy bags. If 6 of these are selected at random by grabbing a handful of these goodies from the bowl, what is the probability that this selection contains 2 cookies and that the rest are fun-size candy bags? (Note: No need to bring your answer in lowest terms. Give the answer as a fraction or as a decimal rounded to four decimal places.)
A major traffic problem in Baguio City can be seen in the intersection of Abanao and Maharlika. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.85 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes. Draw the transition diagram in 2 periods. (TREE DIAGRAM)
In a game of Chuck-a-Luck, a player can bet $1 on any one of the numbers 1, 2, 3, 4, 5, and 6. Three dice are rolled. If the player's number appears k times, where k > 1, the player gets $k back, plus the original stake of $1. Otherwise, the player loses the $1 stake. Some people find this game very appealing. They argue that they have a 1/6 chance of getting their number on each die, so at least a 1/6+1/6+1/6 = 50% chance of doubling their money. That's enough to break even, they figure, so the possible extra payoff in case their number comes up more than once puts the game in their favor. a) What do you think of this reasoning? b) Over the long run, how many cents per game should a player expect to win or lose playing Chuck-a-Luck?
Is Lucas's first free throw shot independent of his second free throw shot? O The two free throws are dependent on each other. O The two free throws are independent of each other. O It is impossible to tell from the given information whether or not the two free throws independent of each other. What is the probability that Lucas makes both free throws?
In the Introduction to Impossibility module, 4/5 of students pass the exam. Of those who pass the exam 9/10 attend lectures, and of those who fail only 1/2 attend lectures. What is the probability that a student who doesn’t attend lectures passes the exam?
I am in possession of two coins. One is fair so that it lands heads (H) and tails (T) with equal probability while the other coin is weighted so that it always lands H. Both coins are magical: if either is flipped and lands H then a $1 bill appears in your wallet, but when it lands T nothing happens. You may only flip a coin once per period. The interest rate is i per period. You are risk-neutral and thus only concern yourself with expected values (and not variance). For simplicity, in the questions below assume you will live forever. Suppose now that I also do not know which coin is fair and which is weighted.You pick one of the two coins at random. (a) What is your willingness to pay for this coin? (b) What is your willingness to pay for "an option" to purchase the coin, where the option works as follows: you may flip the coin once and observe the outcome. Then, if you wish, you may purchase the coin from me for the amount you determined in part 4(a). (c) What is your…
2 - please show the complete solution, thank you!
If a coin is balanced so that p(Heads) = p(Tails) = 1/2, then which of the following outcomes is least likely to occur? Select one: a. 10 Heads in 10 tosses b. 8 Heads in 10 tosses c. 2 Heads in 10 tosses d. 5 Heads in 10 tosses
Could you do question 5?
(1) On their first date, Kelly asks Mike to guess the date of her birth, not including the year. d) If Kelly asks Mike to guess her age, and Mike's guess is too high by 15 years, what is the probability that Mike and Kelly will have a second date?
On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate. b sketch a tree diagram to model this process
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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