In the game Mastermind, one player guesses a four-color code (represented by pegs). There are 9 colors to choose from. The order of the colors matters, and let's say the code has four unique colors. Define the events Y, B, and R as follows: Y: The third peg is yellow. B: The first peg or the third peg is blue. R: The code contains a red peg and white peg consecutively (in that order). a Calculate the probability of each event: p(B), p(R), and p(Y) b What is p(BY)? c What is p(BIR)? d What is p(R/Y)? e Consider all pairs of events: (B,Y). (B, R), and (R,Y). Which pairs are events are independent and which pairs are not independent? Justify your answers using one of the independence tests we learned.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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In the game Mastermind, one player guesses a four-color code (represented by pegs). There are 9 colors to
choose from. The order of the colors matters, and let's say the code has four unique colors. Define the events
Y, B, and R as follows:
Y: The third peg is yellow.
B: The first peg or the third peg is blue.
R: The code contains a red peg and white peg consecutively (in that order).
Transcribed Image Text:In the game Mastermind, one player guesses a four-color code (represented by pegs). There are 9 colors to choose from. The order of the colors matters, and let's say the code has four unique colors. Define the events Y, B, and R as follows: Y: The third peg is yellow. B: The first peg or the third peg is blue. R: The code contains a red peg and white peg consecutively (in that order).
a Calculate the probability of each event: p(B), p(R), and p(Y)
b What is p(BY)?
c What is p(BIR)?
d What is p(R/Y)?
e Consider all pairs of events: (B,Y). (B, R), and (R,Y). Which pairs are events are independent and
which pairs are not independent? Justify your answers using one of the independence tests we learned.
Transcribed Image Text:a Calculate the probability of each event: p(B), p(R), and p(Y) b What is p(BY)? c What is p(BIR)? d What is p(R/Y)? e Consider all pairs of events: (B,Y). (B, R), and (R,Y). Which pairs are events are independent and which pairs are not independent? Justify your answers using one of the independence tests we learned.
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