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
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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Transcribed Image Text: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)=q°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 your answer.
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