4. A man claims to be able to distinguish between two kinds of wine with 90% accuracy and presents his claim to an agency interested in promoting the consumption of one of two kinds of wine. The following experiment is conducted to check his claim. The man is to taste the two types of wine and distinguish between them. This is to be done nine times with a 3-minute break after each taste. Assume that each tasting is independent. It is agreed that if the man is correct at least six out of the nine times, he will be hired. (a) Assume that the man is guessing. What is the likelihood of the man being hired? (b) Assume now that the man's claim is true (i.e. that his probability of success in each tasting is 0.9). What is the chance of the man being hired?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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4. A man claims to be able to distinguish between two kinds of wine
with 90% accuracy and presents his claim to an agency interested in
promoting the consumption of one of two kinds of wine. The following
experiment is conducted to check his claim. The man is to taste the
two types of wine and distinguish between them. This is to be done
nine times with a 3-minute break after each taste. Assume that each
tasting is independent. It is agreed that if the man is correct at least
six out of the nine times, he will be hired.
(a) Assume that the man is guessing. What is the likelihood of the
man being hired?
(b) Assume now that the man's claim is true (i.e. that his probability
of success in each tasting is 0.9). What is the chance of the man
being hired?
Transcribed Image Text:4. A man claims to be able to distinguish between two kinds of wine with 90% accuracy and presents his claim to an agency interested in promoting the consumption of one of two kinds of wine. The following experiment is conducted to check his claim. The man is to taste the two types of wine and distinguish between them. This is to be done nine times with a 3-minute break after each taste. Assume that each tasting is independent. It is agreed that if the man is correct at least six out of the nine times, he will be hired. (a) Assume that the man is guessing. What is the likelihood of the man being hired? (b) Assume now that the man's claim is true (i.e. that his probability of success in each tasting is 0.9). What is the chance of the man being hired?
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