(From Hans Reichenbach's The Theory of Probability, University of California Press, 1949.) Mr. Smith's gardener is notdependable; the probability that he will forget to water the rosebush during Smith's absence is 2/3. The rosebush is inquestionable condition anyhow; if watered, the probability of its withering is 1/2, but if it is not watered, the probability ofits withering is 3/4. Upon returning, Smith finds that the rosebush has withered. What is the probability that the gardenerdid not water the rosebush?

Answered: (From Hans Reichenbach's The Theory of…

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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5.Prove the following properties of probability: P(A) = 1-P(A). b. For any events A and B, P(AUB) = P(A) + P (B) – P(AB). -
Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is 0.27, the probability that "she's up all night for good fun" is 0.39, and the probability that "she's up all night 'til the sun" AND "she's up all night for good fun" is 0.35, what's the probability that "she's up all night 'til the sun"? Round to 2 decimal places as needed. Your Answer: Answer
b.Dick rolls the first “1” before Jane does.?? Only b??
A coin is tossed 4 times and gives four heads in a row. You say “I guess that the fifth toss will result into a head with a probability of 1.”
Could you do question 5?
Suppose that the proportions of blood phenotypes in a particular population are as follows: O A B AB 0.47 0.06 0.02 0.45 Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O? (Enter your answer to four decimal places.) What is the probability that the phenotypes of two randomly selected individuals match? (Enter your answer to four decimal places.)
From experience, a wheat farmer living in Manitoba, Canada finds that his annual profit (in Canadian dollars) is $80,000 if the summer weather is typical, $50,000 if the weather is unusually dry, and $20,000 if there is a severe storm that destroys much of his crop. Weather bureau records indicate that the probability is 0.70 of typical weather, 0.20 of unusually dry weather, and 0.10 of a severe storm. Let X denote the farmer's profit next year (a) Construct a table with the probability distribution of X. (b) What is the probability that the profit is $50,000 or less? (c) Find the mean of the probability distribution of X. Interpret. (d) Suppose the farmer buys insurance for $3000 that pays him $20,000 in the event of a severe storm that destroys much of the crop and pays nothing otherwise. Find the probability distribution of his profit. Find the mean and summarize the effect of buying this insurance.
Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is 0.37, the probability that "she's up all night for good fun" is 0.37, and the probability that "she's up all night 'til the sun" AND "she's up all night for good fun" is 0.34, what's the probability that "she's up all night 'til the sun"?
Chris has just received test results from a patient named Cardi who is infected with a mystery disease. The accuracy of the test is as follows:The probability the test will be positive if Cardi is infected is p, and the probability the test will be positive if Cardi is not infected is q. The proportion of the population that is infected is π. The test comes back positive. Chris has no information about the disease and related symptoms. Suppose Chris does not have a true gasp of the base rates. Chris thinks that the base rate is γπ (gamma*pi), with γ is less than or equal to π. This is to make sure that Chris's belief about the prevalance of the mystery disease is no more than 100%. If p=0.95, 1=0.05, π=1, what must be the value of γ if Chris thinks that the probability Cardi has the disease is 0.9? A. 3.57 B. 0.5 C. 1.05 D. 3.214 Please provide explanation
5. A fair 10-sided die is rolled; let D10 be the number that comes up. Find E[min{D10, 6}]. (If the notation is not clear: min{x,y} just refers to the smaller of the two numbers, x and y. This notation is not unique to probability, but it comes up more often in probability problems.)
Need Parts D and E.
Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is 0.31, the probability that "she's up all night for good fun" is 0.20, and the probability that "she's up all night 'til the sun" AND "she's up all night for good fun" is 0.35, what's the probability that "she's up all night 'til the sun"?

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