3. Jason and Ryan have 25 years of cello experience between the two of them, so they decide to create a band together. They want to make some really unusual music so they decide to choose which sting to play by flipping a fair coin 3 times. If they get 0 heads, they play a C, if they get 1 head they play a D, if they get 2 heads they play a G, and if they get 3 heads they play an A. They repeat this procedure 8 times to make a “song". (a) What is the probability that the first 4 notes are the same (same notes and same order) as the last 4 notes? (b) Suppose that the first 4 notes are the same (same notes same order) as the last 4 notes. What is the probability that the first note is a C?

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3. Jason and Ryan have 25 years of cello experience between the two of them, so they decide
to create a band together. They want to make some really unusual music so they decide to
choose which sting to play by flipping a fair coin 3 times. If they get 0 heads, they play
a C, if they get 1 head they play a D, if they get 2 heads they play a G, and if they get 3
heads they play an A. They repeat this procedure 8 times to make a “song".
(a) What is the probability that the first 4 notes are the same (same notes and same order)
as the last 4 notes?
(b) Suppose that the first 4 notes are the same (same notes and same order) as the last 4
notes. What is the probability that the first note is a C?
Transcribed Image Text:3. Jason and Ryan have 25 years of cello experience between the two of them, so they decide to create a band together. They want to make some really unusual music so they decide to choose which sting to play by flipping a fair coin 3 times. If they get 0 heads, they play a C, if they get 1 head they play a D, if they get 2 heads they play a G, and if they get 3 heads they play an A. They repeat this procedure 8 times to make a “song". (a) What is the probability that the first 4 notes are the same (same notes and same order) as the last 4 notes? (b) Suppose that the first 4 notes are the same (same notes and same order) as the last 4 notes. What is the probability that the first note is a C?
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