Should Manami choose the three-man jury or the one-man jury?
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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Question
Manami is given a choice: she can have her performance assessed either by a three-
man jury or a one-man jury. The three-man jury consists of two members who are
both known to be impressed by her singing skills, each having probability 2/3 of giving
her a passing vote, plus a third member that flips a coin for each decision (the
majority rules). On the other hand, the one-man jury is by himself impressed with
Manami and has probability 2/3 of giving her a passing vote. Should Manami choose
the three-man jury or the one-man jury? (Hint: there are two scenarios in which
Manami passes the three-man jury, first being when the first two members agree,
and the second being when they split, but the third member’s coin toss results in
giving Manami a pass. What is the probability of either of these two scenarios
happening?)
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