3. A food company is conducting research on customers' taste. In each round of a blind taste experiment four black teas and one herbal tea are presented to participants. Suppose that the participants randomly guess, independently in each round. If a participant picks the herbal tea in each of three rounds, a box of tea is won. Let X be the number of participants until a box of tea is won. (a) If pis the probability that a participant wins a box of tea, write the formula P(X = 1)+ P(X = 2)+ P(X = 3) in terms of p and q =1-p, then show that P(X > 3) =q'. (b) Describe P(X =10/X >3) in words, then write its formula in terms of P(X =10) and P(X > 3). Using that formula, show that P(X 10/X>3)=Dq°p. (c) Using a similar idea to that in (b), try to guess (in terms of p and q) the probability that there is no winner until the 100th participant, knowing that there is still no winner up to 90th participant,. (d) What is the expected number of participants until a box of tea is won. If the experiment goes with no winner until 50th participant, is the winner lucky enough? Explain vour answer
3. A food company is conducting research on customers' taste. In each round of a blind taste experiment four black teas and one herbal tea are presented to participants. Suppose that the participants randomly guess, independently in each round. If a participant picks the herbal tea in each of three rounds, a box of tea is won. Let X be the number of participants until a box of tea is won. (a) If pis the probability that a participant wins a box of tea, write the formula P(X = 1)+ P(X = 2)+ P(X = 3) in terms of p and q =1-p, then show that P(X > 3) =q'. (b) Describe P(X =10/X >3) in words, then write its formula in terms of P(X =10) and P(X > 3). Using that formula, show that P(X 10/X>3)=Dq°p. (c) Using a similar idea to that in (b), try to guess (in terms of p and q) the probability that there is no winner until the 100th participant, knowing that there is still no winner up to 90th participant,. (d) What is the expected number of participants until a box of tea is won. If the experiment goes with no winner until 50th participant, is the winner lucky enough? Explain vour answer
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Recommended textbooks for you
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage