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Binomial Theorem and Bayes Theorem 10 1. Find the binomial expansion of the expression 2. Which member of the binomial expansion of the algebraic expression 2x- contains x* ? 3. Find two intermediate members of the binomial expansion of the expression (x+y)³. 4. Find intermediate members of the binomial expansion of the expression (x+y)+ 5. Find: a) The fifth member of the binomial expansion of expression (x - y) b) The ninth member of the binomial expansion of expression 6. Find the intermediate member of the binomial expansion of the expression (√x-1). X 2√x 12 7. Which member of the binomial expansion of the algebraic expression √²+√x contains x²? 8. For what value of x the fifth member of the binomial expansion of the algebraic 10 1 expression equals to the number 105 ?

Binomial Theorem and Bayes Theorem 10 1. Find the binomial expansion of the expression 2. Which member of the binomial expansion of the algebraic expression 2x- contains x* ? 3. Find two intermediate members of the binomial expansion of the expression (x+y)³. 4. Find intermediate members of the binomial expansion of the expression (x+y)+ 5. Find: a) The fifth member of the binomial expansion of expression (x - y) b) The ninth member of the binomial expansion of expression 6. Find the intermediate member of the binomial expansion of the expression (√x-1). X 2√x 12 7. Which member of the binomial expansion of the algebraic expression √²+√x contains x²? 8. For what value of x the fifth member of the binomial expansion of the algebraic 10 1 expression equals to the number 105 ?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Exercises Binomial Theorem and Bayes Theorem 10 ^{(x-1)²⁰. 1. Find the binomial expansion of the expression x- 2. Which member of the binomial expansion of the algebraic expression 2x- contains x* ? 3. Find two intermediate members of the binomial expansion of the expression (x+y)³. 4. Find intermediate members of the binomial expansion of the expression (x+y)+ 5. Find: a) The fifth member of the binomial expansion of expression (x−y) 1 b) The ninth member of the binomial expansion of expression x² 6. Find the intermediate member of the binomial expansion of the expression (√x-1). X 7. Which member of the binomial expansion of the algebraic expression 12 14 X 12 (√²+√x¹² contains x²? 8. For what value of x the fifth member of the binomial expansion of the algebraic 10 1 1 expression equals to the number 105 ? 2√x 2 9. Find out which member of the binomial expansion of the algebraic expression 8 1 (x²- equals to the number 70. 10. Find out which member of the binomial expansion of the algebraic expression is the product of the coeficient and of the unknown √x. 11. A particular study showed that 12% of men will likely develop colon cancer. A man with colon cancer has a 95% chance of a positive test result from a medical screening exam. A man without colon cancer has a 6% chance of getting a false positive test result. What is the probability that a man has cancer given that he has a positive test result? 12. In a particular pain clinic, 10% of patients are prescribed narcotic pain killers. Overall, 5% of the clinic's patients are addicted to narcotics (including pain killers and illegal substances). Out of all the people prescribed pain pills, 8% are addicts. If a patient is an addict, what is the probability that they will be prescribed pain pills?
Transcribed Image Text:Exercises Binomial Theorem and Bayes Theorem 10 ^{(x-1)²⁰. 1. Find the binomial expansion of the expression x- 2. Which member of the binomial expansion of the algebraic expression 2x- contains x* ? 3. Find two intermediate members of the binomial expansion of the expression (x+y)³. 4. Find intermediate members of the binomial expansion of the expression (x+y)+ 5. Find: a) The fifth member of the binomial expansion of expression (x−y) 1 b) The ninth member of the binomial expansion of expression x² 6. Find the intermediate member of the binomial expansion of the expression (√x-1). X 7. Which member of the binomial expansion of the algebraic expression 12 14 X 12 (√²+√x¹² contains x²? 8. For what value of x the fifth member of the binomial expansion of the algebraic 10 1 1 expression equals to the number 105 ? 2√x 2 9. Find out which member of the binomial expansion of the algebraic expression 8 1 (x²- equals to the number 70. 10. Find out which member of the binomial expansion of the algebraic expression is the product of the coeficient and of the unknown √x. 11. A particular study showed that 12% of men will likely develop colon cancer. A man with colon cancer has a 95% chance of a positive test result from a medical screening exam. A man without colon cancer has a 6% chance of getting a false positive test result. What is the probability that a man has cancer given that he has a positive test result? 12. In a particular pain clinic, 10% of patients are prescribed narcotic pain killers. Overall, 5% of the clinic's patients are addicted to narcotics (including pain killers and illegal substances). Out of all the people prescribed pain pills, 8% are addicts. If a patient is an addict, what is the probability that they will be prescribed pain pills?
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