Q. 8. What is the chance that a. leap year selected at random wilcontain 53 Sundays?[Hint : A leap year consists of 53 complete weeks and 2 days overThese two days can be](1) Monday & Tuesday.(2) Tuesday & Wednesday(3) Wednesday & Thursday(4) Thursday & Friday(5) Friday & Saturday(6) Saturday & Sunday(7) Sundary & MondayHence P=2/7

Answered: Q. 8. What is the chance that a. leap…

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* A medical researcher estimates that 2% of a population is infected with a rare disease which for this problem we will assume is accurate. The procedure used for testing for this disease is 90% accurate. So, if one has the disease, the test will indicate that 90% of the time, and if the person doesn't have the disease, the test will indicate that 90% of the time. Of course, what this means is that the test will give a false positive result 10% of the time. If a person is picked at random and tested: (a) What is the probability that the person tests positive? (b) What is the probability that if a person tested positive for the disease he or she actually had the disease?
V. (10) The following table of 850 students shows those that have or don't have covid-19 and shows those who had a positive test or a negative test. I just made this data up so don't take this as representative of our current state. Answer the following questions. Negative Test 5 Positive Test Have Covid-19 45 Don't have Covid-19 25 775 Let D be the event you Don't have Covid-19 and N the event you have a negative test. 1. P(D) = 2. P(D I N) = 3. Are D and N independent? 5. What is the probability that you Have Covid-19 even though the test came back negative? 4. Explain TI-84 Plus TEXAS INSTRUMENTS
1. A machine can be in one of four states: 'running smoothly' (state 1), 'running but needs adjustment' (state 2), 'temporarily broken' (state 3), and 'destroyed' (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. • If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine…
1. Suppose a fair coin is tossed 5 times. (a) What is the probability that we observe the sequence H, T, H, H,T? (b) What is the probability that we observe exactly 3 heads? (c) If we know that 3 heads were obtained in 5 tosses, what is the probability of the sequence H, T, H, H, T?
1. A machine can be in one of four states: 'running smoothly' (state 1), 'running but needs adjustment' (state 2), 'temporarily broken' (state 3), and 'destroyed' (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. • If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine…
12. Bob and Alice enter an archery contest. Bob hits his target with probability p, 0< p<1, and Alice hits her target, independently of Bob, with probability q, 0
Example 1.12 I play a gambling game in which I will win k – 2 dollars with probability - for any k E N, that is, • with probability ,1 lose 1 dollar; • with probability , 1 win 0 dollar; • with probability I win 1 dollar; • with probability • with probability ,I win 2 dollars; ,I win 3 dollars; 32' What is the probability that I win more than or equal to 1 dollar and less than 4 dollars? What is the probability that I win more than 2 dollars?
4 hey can you help me answer this question below please Try to explain your results: e.g. why there is a positive, negative or no comovement between the two variables
7) In a back yard vineyard in Napa valley with 10 grape vines in a row, if the weather works well (just right), rain in the spring and dry through summer, the yield for each vine is distributed roughly binomial with N=800, p=.71 . In a drought the yield is Binomial with N=800 and P=.6, while if the year is too wet, the yield of useful grapes per vine is N=700, P=.78. Under climate change the probability of a just right year is about .05, of a too wet year is .15, and a dry year is .8. On a just right year the wine can sell for 200 dollars/bottle, on a dry year the quality drops so it will sell for 100 dollars a bottle, on wet year it will sell for 25 dollars a bottle. (The yield for all 10 vines was more than 5600 grapes. (use the normal approximation to the binomial) Given this yield: What is the probability that you will be able to sell for 200 dollars a bottle?

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