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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An actuary is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of women. For each of the three factors, the probability is 0.1 that a woman in the population has only this risk factor (and no others). For any two of the three factors, the probability is 0.12 that she has exactly these two risk factors (but not the other). The probability that a woman has all three risk factors, given that she has A and B, is 1/3 . What is the probability that a woman has none of the three risk factors, given that she does not have risk factor A? A) 0.280 B) 0.311 C) 0.467 D) 0.484 E) 0.700
Rework problem 9 from section 2.4 of your text. Assume that 9 people, including Tom and Jerry, apply for 5 sales positions. People are hired at random. (1) What is the probability that both Tom and Jerry are hired? (2) What is the probability that one is hired and one is not?
12. An actuary is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of women. For each of the three factors, the probability is 0.1 that a woman in the population has only this risk factor (and no others). For any two of the three factors, the probability is 0.12 that she has exactly these two risk factors (but not the other). The probability that a woman has all three risk factors, given that she has A and B, is 1/3. Calculate the probability that a woman has none of the three risk factors, given that she does not have risk factor A. (A) 0.280 (B) 0.311 (C) 0.467 (D) 0.484 (E) 0.700 4
1. The basketball coach says that based on Noah's free throws this season, Noah has a 3/4 probability of making each free throw. Select all the ways Noah could accurately simulate the number of free throws he will make in his next 6 attempts. *
16. JTWO rescue crews set out to find a lost hiker in the Kern Canyon. Suppose the first crew has a 30% chance of finding the lost hiker before nightfall and the second crew has a 40% chance of finding the lost hiker before nightfall. If the two crews work independently, what is the probability that the lost hiker is found before nightfall?
QUESTION 9 Suppose a box contains 20 marbles, 6 are red, 5 are blue, and 9 are yellow. Find the requested probabilities. Leave your answer as an unsimplified fraction. a. If two marbles are selected with replacement, what is the probability that one is red and the other is yellow? (hint: order is not specific so you could choose a red then yellow or yellow then red). b. If two marbles are selected without replacement, what is the probability that one is red and the other is yellow? c. If 5 marbles are selected without replacement, what is the probability that they are all yellow?
Rework problem 22 from section 3.2 of your text, involving the colored balls. For this problem, assume the box contains 9 blue balls, 7 white balls, and 4 red balls, and that we choose two balls at random from the box. What is the probability of neither being blue given that neither is white?
Suppose that each time Bar-bie throws a dart, she has a 3/4 probability of getting a bullseye. If Barbie shoots three darts, what is the probability that she gets a bullseye on at least two of them?
2 - please show the complete solution, thank you!
Could you do question 5?
the accident. Question 16 Shashank performs an experiment comprising a series of independent trials. On each trial, he simultaneously flips a set of Z fair coins. a. Given that Shashank has just had a trial with Z tails, what is the probability that next two trials will also have this result? b. Whenever all the Z coins land on the same side in any given trial, Shashank calls the trial a success. i. Find the PMF for K, the number of trials up to, but not including the second success. Find the expectation and variance of M, the number of tails that occur before the first success where Z = 3 in this case. ii. (Hint: Write M = X, + X2 + .…+ Xy Where X; is number of tails in that occur on unsuccessful trail i and N is number of unsuccessful trails and find E (M) in terms of E (X) and E(N) and for var(M) first write in terms of M | N (i.e. M given N) and later write var(M) in terms of E(N), E (X), var(N), var(X) using the above derived variance equation in terms of M | N.) You are expected…
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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